Information processing method, information processing system, and program

Abstract

This information processing method is performed by a computer and comprises: a step (S101) for acquiring first information pertaining to two or more types of a plurality of polyhedrons having mutually different shapes; a step (S102 to S106) for generating, on the basis of the first information, second information pertaining to a 3-dimensional structure in which a plurality of polyhedrons are arranged; and a step (S107) for outputting the generated second information. The 3-dimensional structure is a structure in which the plurality of polyhedrons are arranged without a gap.

Description

Information processing method, information processing system, and program

[0001] The present disclosure relates to a technique for generating a three-dimensional structure.

[0002] Space filling (tiling, or tessellation) is the operation of filling a space with figures without gaps. For example, space filling in two-dimensional space is called plane tessellation, which is the operation of filling two-dimensional space with plane figures without gaps.

[0003] Patent Document 1 discloses a method for generating a three-dimensional solid.

[0004] Patent Document 2 discloses a method for simulating a house structure.

[0005] Non-Patent Document 1 discloses a polyhedron code and a polytopon code.

[0006] Special table 2018-516794 publication Special table 2021-501934 publication

[0007] Kengo, N. , & Takahide, M. (2016). How to describe disordered structures, Scientific Reports, 6, 23455.

[0008] The present disclosure provides an information processing method and the like that can generate a space-filling structure in a three-dimensional space.

[0009] An information processing method according to one aspect of the present disclosure is an information processing method executed by a computer, and includes the steps of: acquiring first information about a plurality of polyhedrons, the plurality of polyhedrons including two or more types of polyhedrons having different shapes; generating second information about a three-dimensional structure in which the plurality of polyhedrons are arranged based on the first information; and outputting the generated second information, wherein the three-dimensional structure is a structure in which the plurality of polyhedrons are arranged without any gaps.

[0010] According to the present disclosure, space-filling structures can be generated in three-dimensional space.

[0011] FIG. 1 is a diagram showing an example of a three-dimensional structure generated from a plurality of polyhedrons. FIG. 2 is a diagram showing another example of a three-dimensional structure generated from a plurality of polyhedrons. FIG. 3 is a diagram showing yet another example of a three-dimensional structure generated from a plurality of polyhedrons. FIG. 4 is a diagram showing an example of a crystal structure generated from a three-dimensional structure. FIG. 5 is a block diagram showing an overall configuration including an information processing system according to embodiment 1. FIG. 6 is a diagram showing an example of polyhedron data stored in a first storage unit. FIG. 7 is a diagram showing an example of second information stored in a second storage unit. FIG. 8 is a diagram showing an image displayed on a display unit in a first use example of embodiment 1. FIG. 9 is a diagram showing an image displayed on a display unit in a first use example of embodiment 1. FIG. 10 is a diagram showing a list of Bravais lattices. FIG. 11 is a diagram showing an image displayed on a display unit in a second use example of embodiment 1. FIG. 12 is a diagram showing an example of symmetry of a three-dimensional structure. FIG. 13 is a diagram showing an image displayed on a display unit in a third use example of embodiment 1. FIG. 14 is a diagram showing an image displayed on a display unit in a fourth use example of embodiment 1. FIG. 15 is a diagram showing an image displayed on a display unit in a fifth use example of embodiment 1. FIG. 16 is a diagram showing an example of the distortion of a polyhedron. FIG. 17 is a diagram showing an example of a three-dimensional structure having distortion. FIG. 18 is a flowchart showing an example of the operation of the information processing system according to the first embodiment. FIG. 19 is a flowchart showing an example of a process for generating a polyhedron code from a polyhedron. FIG. 20 is a diagram showing an example of a process for generating a polyhedron code from a regular tetrahedron. FIG. 21 is a diagram showing an example of a process for generating a polyhedron code from a regular octahedron. FIG. 22 is a diagram showing an example of a process for generating a polyhedron code from a cuboctahedron. FIG. 23 is a flowchart showing an example of a process for generating a polyhedron code from a polyhedron code. FIG. 24 is a flowchart showing an example of a process for generating a three-dimensional structure from a polyhedron code. FIG. 25 is a diagram showing a specific example of a polyhedron code. FIG. 26 is a diagram showing a specific example of a process for generating a three-dimensional structure from a polyhedron code. FIG. 27 is a sequence diagram showing an example of the operation of the information processing system according to the first embodiment, the display unit, the first storage unit, and the second storage unit.FIG. 28 is a flowchart showing another example of operation of the information processing system according to the first embodiment. FIG. 29 is a diagram showing a specific example of a process for converting a polyhedron into a polyhedral graph. FIG. 30 is a diagram showing a specific example of converting a periodic graph into a three-dimensional structure. FIG. 31 is a diagram showing an image displayed on the display unit in a first use example of the second embodiment. FIG. 32 is a diagram showing an image displayed on the display unit in the first use example of the second embodiment. FIG. 33 is a diagram showing an image displayed on the display unit in the first use example of the second embodiment. FIG. 34 is a sequence diagram showing a first example of operation of the information processing system according to the second embodiment, and the display unit, first storage unit, and second storage unit. FIG. 35 is a diagram showing an image displayed on the display unit in a second use example of the second embodiment. FIG. 36 is a diagram showing an image displayed on the display unit in the second use example of the second embodiment. FIG. 37 is a sequence diagram showing a second example of operation of the information processing system according to the second embodiment, and the display unit, first storage unit, and second storage unit. FIG. 38 is a block diagram showing an overall configuration including an information processing system according to the third embodiment. FIG. 39 is a diagram showing an image displayed on the display unit in a use example of the third embodiment. Fig. 40 is a diagram showing an example of a three-dimensional structure related to a building. Fig. 41 is a diagram showing an example of a three-dimensional structure related to an ornament. Fig. 42 is a diagram showing an example of a three-dimensional structure related to an interior. Fig. 43 is a diagram showing an example of a three-dimensional structure related to a toy. Fig. 44 is a diagram showing an example of a three-dimensional structure related to an urban design. Fig. 45 is a diagram showing an example of a three-dimensional structure related to storage. Fig. 46 is a diagram showing an example of a three-dimensional structure related to food. Fig. 47 is a diagram showing an example of a three-dimensional structure related to materials. Fig. 48 shows the faces of a regular tetrahedron. １ FIG. 49 shows the sides a, b, and c of the regular tetrahedron. １ FIG. 50 shows the faces of a regular octahedron. １ FIG. 51 shows the sides a, b, and c of the regular octahedron. ２ FIG. 52 shows the faces of a regular octahedron. ５ FIG. 53 shows the faces of a regular octahedron. ６ FIG. 54 shows the faces of a cuboctahedron. １ FIG. 55 shows the sides a, b, and c of the cuboctahedron.２ FIG. 56 shows the faces of a cuboctahedron. ６ FIG. 57 shows the faces of a cuboctahedron. ７ FIG.

[0012] (Findings that led to the present disclosure) Many space-filling structures in two-dimensional space have been discovered in the past. Meanwhile, new space-filling structures in two-dimensional space made of pentagons have been reported in recent years, and even among space-filling structures in two-dimensional space that have been used for a long time, there are still unknown space-filling structures.

[0013] In addition to space-filling structures in two-dimensional space, space-filling structures also exist in three-dimensional space. Hereinafter, a space-filling structure in three-dimensional space will be referred to as a "three-dimensional structure." A three-dimensional structure is a structure in which multiple solids, such as polyhedra, are tightly packed in three-dimensional space. In particular, a three-dimensional structure here refers to a structure in which multiple polyhedra are tightly arranged in three-dimensional space. Furthermore, a three-dimensional structure refers to a structure in which multiple polyhedra, including two or more types of polyhedra with different shapes, are tightly arranged in three-dimensional space. Note that "multiple polyhedra are tightly arranged" means that, for any one of the multiple polyhedra, the vertices of the faces that contact other polyhedra are located at the same positions as the vertices of the faces of the other polyhedra that contact the polyhedron. Furthermore, even if two polyhedra have the same number of faces, if their skewness or size differ, they are equivalent to two types of polyhedra with different shapes.

[0014] For example, in recent years, three-dimensional structures have begun to be applied to describe the structure of materials. Specifically, the structure of a material refers to the microstructure of a material such as a crystalline material or an amorphous material. In particular, in the structure of an inorganic material, an atom coordinates with multiple neighboring atoms and exists surrounded by them. Furthermore, the structure of an inorganic material is composed of polyhedra (coordination polyhedra) formed by connecting the centers of multiple neighboring atoms, filling a three-dimensional space without gaps. In other words, the structure of an inorganic material can be considered a three-dimensional structure.

[0015] In addition, there are a wide variety of three-dimensional structures depending on the combination of the filled coordination polyhedra. Figure 1 is a diagram showing an example of a three-dimensional structure generated from a plurality of polyhedra. For example, the three-dimensional structure generated from two regular tetrahedrons and one regular octahedron shown in Figure 1 (a) has two types of structures, namely, a face-centered cubic lattice structure (fcc type structure) shown in Figure 1 (b) and a hexagonal close-packed structure (hcp type structure) shown in Figure 1 (c), due to the difference in stacking. Figure 2 is a diagram showing another example of a three-dimensional structure generated from a plurality of polyhedra. For example, although it is composed of one type of polyhedron, the three-dimensional structure generated from one regular tetrahedron shown in Figure 2 (a) has two types of structures, namely, a body-centered cubic lattice structure (bcc type structure) shown in Figure 2 (b) and a MgCu structure shown in Figure 2 (c), due to the difference in stacking. ２ There are two types of structures: a perovskite structure and a cubic octahedron structure. Figure 3 is a diagram showing yet another example of a three-dimensional structure generated from a plurality of polyhedra. For example, the three-dimensional structure generated from one regular octahedron and one cubic octahedron shown in Figure 3(a) includes the perovskite structure shown in Figure 3(b). Note that although Figure 3(b) shows one cubic octahedron, in reality, multiple cubic octahedrons are arranged without gaps around the central regular octahedron.

[0016] Furthermore, three-dimensional structures have the potential to be applied not only to material structures but also to a variety of other applications, such as the design of buildings.

[0017] However, finding an unknown three-dimensional structure is difficult.

[0018] For example, Patent Document 1 discloses a method for generating a three-dimensional space figure that allows gaps, but does not disclose a method for generating a three-dimensional structure in which multiple polyhedrons are arranged without gaps.

[0019] For example, Patent Document 2 discloses a method for generating housing structure data by combining three-dimensional blocks and simulating the housing structure using the housing structure data. However, Patent Document 2 only discloses housing structure data by combining three-dimensional blocks of the same shape, and does not disclose a method for generating a three-dimensional structure using two or more types of polyhedrons with different shapes.

[0020] Furthermore, Non-Patent Document 1 discloses a polyhedron code that describes a polyhedron by a numerical sequence and a polyhedron code that describes a polyhedron by a numerical sequence. However, Non-Patent Document 1 does not disclose a technique for using these codes to generate a three-dimensional structure in which multiple polyhedrons are arranged without gaps.

[0021] In order to solve the above problem, an information processing method according to one aspect of the present disclosure is an information processing method executed by a computer, and includes the steps of: acquiring first information about a plurality of polyhedrons, the plurality of polyhedrons including two or more types of polyhedrons having different shapes; generating second information about a three-dimensional structure in which the plurality of polyhedrons are arranged based on the first information; and outputting the generated second information, wherein the three-dimensional structure is a structure in which the plurality of polyhedrons are arranged without any gaps.

[0022] This allows the generation of space-filling structures in three-dimensional space.

[0023] Also, for example, the second information may include at least one of information indicating the three-dimensional structure, information indicating a sequence including numbers or letters representing the three-dimensional structure, and information indicating a periodic graph representing the three-dimensional structure.

[0024] This allows the generation of space-filling structures in three-dimensional space.

[0025] Furthermore, in the step of acquiring the first information, shape information indicating the shape of each of the plurality of polyhedrons may be acquired as the first information, and in the step of generating the second information, the second information may be generated regarding the three-dimensional structure in which the plurality of polyhedrons having the shape indicated by the shape information are arranged without any gaps.

[0026] This makes it possible to generate a space-filling structure in three-dimensional space, for example, under the constraints of the shapes of multiple polyhedrons specified by the user, making it easier to generate the space-filling structure in three-dimensional space that the user desires.

[0027] Furthermore, in the step of acquiring the first information, quantity information indicating the number of each shape of the plurality of polyhedrons may be further acquired as the first information, and in the step of generating the second information, the second information may be generated regarding the three-dimensional structure in which the plurality of polyhedrons of the shape indicated by the shape information are arranged without gaps in the number of each shape indicated by the quantity information.

[0028] This makes it possible to generate a space-filling structure in three-dimensional space, for example, under constraints on the number of each shape of multiple polyhedrons specified by the user, making it easier to generate the space-filling structure in three-dimensional space that the user desires.

[0029] Furthermore, in the step of acquiring the first information, composition ratio information indicating the composition ratio for each shape of the plurality of polyhedrons may be further acquired as the first information, and in the step of generating the second information, the second information may be generated regarding the three-dimensional structure in which the plurality of polyhedrons of the shapes indicated by the shape information are arranged without gaps at the composition ratio for each shape indicated by the composition ratio information.

[0030] This makes it possible to generate a space-filling structure in three-dimensional space, for example, under constraints on the composition ratio of each of multiple polyhedron shapes specified by the user, making it easier to generate the space-filling structure in three-dimensional space that the user desires.

[0031] Furthermore, in the step of acquiring the first information, distortion information indicating an allowable distortion of the shapes of the plurality of polyhedrons may be further acquired as the first information, and in the step of generating the second information, second information regarding the three-dimensional structure in which at least a portion of the plurality of polyhedrons is distorted so as not to exceed the distortion indicated by the distortion information may be generated.

[0032] This makes it possible to generate a space-filling structure in three-dimensional space, for example, under the constraint of the allowable distortion of the shapes of multiple polyhedrons specified by the user, making it easier to generate the space-filling structure in three-dimensional space that the user desires.

[0033] Furthermore, the skewness may be determined based on the shape of the polyhedron indicated by the shape information, and on at least one of the position of the center of gravity of the polyhedron, the position of at least one vertex of the polyhedron, the length of at least one side of the polyhedron, the angle formed by at least two sides of the polyhedron, and the area of ​​at least one face of the polyhedron.

[0034] This makes it possible to generate a space-filling structure in three-dimensional space, for example, under the constraint of the allowable distortion of the shapes of multiple polyhedrons specified by the user, making it easier to generate the space-filling structure in three-dimensional space that the user desires.

[0035] The method may further include a step of acquiring third information regarding the use of the three-dimensional structure, and in the step of generating the second information, the second information regarding the three-dimensional structure may be generated by adding information based on the use indicated by the third information to the three-dimensional structure generated based on the first information.

[0036] This makes it possible to generate a space-filling structure in three-dimensional space that suits the purpose specified by the user, making it easy to generate a space-filling structure in three-dimensional space that the user desires.

[0037] In addition, the step of generating the second information may include a step of converting the acquired first information into a plurality of first number sequences each representing the plurality of polyhedra, and a step of converting a second number sequence representing a polyhedron generated using the converted plurality of first number sequences into the three-dimensional structure.

[0038] This makes it possible to comprehensively generate space-filling structures in three-dimensional space from information on multiple polyhedra.

[0039] In addition, the step of generating the second information may include the steps of converting the acquired first information into a plurality of polyhedron graphs each representing one of the plurality of polyhedra, and converting a periodic graph generated using the converted polyhedron graphs into the three-dimensional structure.

[0040] This makes it possible to comprehensively generate space-filling structures in three-dimensional space using various methods from information on multiple polyhedra.

[0041] In addition, an information processing system according to one aspect of the present disclosure includes a display unit that displays a first image that accepts input of first information regarding a plurality of polyhedrons, including two or more types of polyhedrons that differ from each other in shape, and a display control unit that causes the display unit to display a second image that represents second information regarding a three-dimensional structure in which the plurality of polyhedrons are arranged, the second image being generated based on the input first information, and the three-dimensional structure is a structure in which the plurality of polyhedrons are arranged without any gaps.

[0042] This allows the user to check the generated space-filling structure in the three-dimensional space.

[0043] In addition, the display unit may further display a third image that accepts input of third information regarding the use of the three-dimensional structure, and the three-dimensional structure may be a structure that is generated based on the input first information and is provided with information based on the use indicated by the input third information.

[0044] This allows the user to check the space-filling structure in three-dimensional space according to the desired application.

[0045] In addition, a program according to one aspect of the present disclosure causes a computer to execute the steps of acquiring first information about a plurality of polyhedrons, the plurality of polyhedrons including two or more types of polyhedrons having different shapes from each other, generating second information about a three-dimensional structure in which the plurality of polyhedrons are arranged based on the first information, and outputting the generated second information, wherein the three-dimensional structure is a structure in which the plurality of polyhedrons are arranged without any gaps.

[0046] This allows the generation of space-filling structures in three-dimensional space.

[0047] Furthermore, the information processing method of the present disclosure can be realized as a computer program that causes a computer to execute the characteristic processes included in the information processing method of the present disclosure. Needless to say, such a computer program can be distributed on a computer-readable non-transitory recording medium such as a CD-ROM or via a communication network such as the Internet.

[0048] That is, according to the technology of the present disclosure, by inputting information on a plurality of polyhedra, it becomes possible to comprehensively generate three-dimensional structures formed by combining the inputted plurality of polyhedra.

[0049] Hereinafter, the embodiments will be specifically described with reference to the drawings.

[0050] Note that the embodiments described below all represent comprehensive or specific examples of the present disclosure. The numerical values, shapes, materials, components, component placement and connection configurations, steps, and step order shown in the following embodiments are merely examples and are not intended to limit the present disclosure. Furthermore, among the components in the following embodiments, components that are not described in the independent claims that represent the highest concept are described as optional components. Furthermore, in all embodiments, the respective contents can be combined. Furthermore, each figure is a schematic diagram and is not necessarily an exact illustration. Furthermore, the same components are designated by the same reference numerals in each figure.

[0051] Furthermore, the information processing system according to the embodiment of the present disclosure may be configured so that all components are included in one computer, or may be configured as a system in which multiple components are distributed across multiple computers.

[0052] First Embodiment An information processing system 100 (information processing method or program) according to a first embodiment of the present disclosure will be described in detail below with reference to the drawings. In the first embodiment, the three-dimensional structure is a structure that becomes a crystalline structure when atoms are arranged. That is, in the first embodiment, the three-dimensional structure is used for materials such as inorganic materials.

[0053] [Generation of Three-Dimensional Structure] First, before describing the first embodiment in detail, the generation of a three-dimensional structure in the information processing method of the present disclosure will be described. In the information processing method of the present disclosure, the three-dimensional structure is represented as a sequence or a graph, thereby achieving comprehensive generation of three-dimensional structures. Note that the "sequence" here includes not only numbers but also characters that replace numbers such as alphabets.

[0054] Hereinafter, a sequence of numbers representing a three-dimensional structure may also be referred to as an "inorganic gene." Examples of inorganic genes include the polyvesicular code proposed by K. Nishio et al., the Systre Key or D-Symbol proposed by O. Delgado-Friedrichs et al., or CRYSTAL-SELFIES, which is an application of SELFIE, which can represent molecular structures as alphabetic strings and is proposed by M. Krenn et al., to three-dimensional structures. In other words, an inorganic gene is, for example, a polyvesicular code that can be converted into a three-dimensional structure.

[0055] As an example, the polycystic code for the A-type zeolite (LTA) structure is "OHG ４ (HG) ４ In this sequence, "O", "H", and "G" are called polyhedron codes, and are sequences determined by the input polyhedron. For example, "O" means a truncated octahedron, and "46 ４ (46) ４ For example, "H" means a cube and is represented by the sequence "46". For example, "G" means a truncated cuboctahedron and is represented by the sequence "6(48) ３ (64) ６ (84) ３ It is expressed as the number sequence "6".

[0056] By changing the arrangement of this polyhedron code, it is possible to generate different 3D structures composed of the same multiple polyhedra. Furthermore, by changing the polyhedron code, it is possible to express any polyhedron. In this way, by using inorganic genes such as the polyhedron code, it is possible to comprehensively generate 3D structures from information on multiple polyhedra.

[0057] In the three-dimensional structure thus generated, it is possible to generate a crystal structure from the three-dimensional structure by appropriately arranging atoms at the center and vertices of each polyhedron. FIG. 4 shows an example of a crystal structure generated from the three-dimensional structure. For example, the three-dimensional structure shown in FIG. 4(a) (in the polyhedron code, "3 ４ (3 ６ ) ４ (3 ４ ) ６ 3 ４ From this, it is possible to generate the crystal structure shown in FIG. 4(b).

[0058] Generally, molecular structures can be expressed as graphs. That is, molecular structures can be expressed as graph structures in which the "atoms" that constitute a compound are "nodes" and the "bonds between atoms" are "edges" that connect the nodes. For example, an example of expressing a molecular structure as a graph and generating a molecular structure is disclosed in Japanese Patent Laid-Open No. 2021-081769.

[0059] On the other hand, crystal structures must be represented by periodic graphs rather than ordinary graphs. A periodic graph, also known as a crystal net, is a three-dimensionally periodic graph. Here, "three-dimensionally periodic" means that there are three linearly independent translations. Generally, a crystal structure can be converted into a periodic graph by defining the atomic bonds in the crystal structure. Furthermore, by using the Kotani-Sunada theory (Kotani-Sunada, 2000, Trans. Amer. Mat.), a periodic graph can be uniquely converted into a crystal structure. For example, a periodic graph with two independent nodes and four edges connecting them, as shown in Figure 4(c), can be converted into a diamond-shaped structure shown in Figure 4(d). In other words, a periodic graph is a graph that has a structure in which multiple polyhedra are arranged without gaps and can be converted into a three-dimensional structure that becomes a crystal structure when atoms are arranged.

[0060] [Information Processing System] Next, the configuration of the information processing system used in the first embodiment will be described.

[0061] 5 is a block diagram showing an overall configuration including an information processing system 100 according to the first embodiment. The information processing system 100 is configured as a computer such as a personal computer or a server. That is, the information processing system 100 may be realized by cloud computing, for example. In the first embodiment, the information processing system 100 will be described as being a stationary computer.

[0062] The information processing system 100 includes an acquisition unit 11, a generation unit 12, and an output unit 13. The information processing system 100 is also connected to an input unit 2, a display control unit 30, a display unit 3, a first storage unit 4, and a second storage unit 5. The input unit 2, the display control unit 30, and the display unit 3 are configured by an information terminal used by a user, such as a smartphone, a tablet terminal, or a personal computer. The input unit 2, the display control unit 30, and the display unit 3 may be the input unit, the display control unit, and the display unit included in the information terminal used by the user.

[0063] The input unit 2, the display control unit 30, the first memory unit 4, and the second memory unit 5 may all be connected to the information processing system 100 via a LAN (Local Area Network) or the like, or may be connected to the information processing system 100 via a network such as the Internet.

[0064] The input unit 2 is an input interface that accepts user input and is configured, for example, with a keyboard, a touch sensor, a touchpad, or a mouse. The input unit 2 accepts input operations by the user and outputs a signal corresponding to the input operation to the information processing system 100. In the present disclosure, the display unit 3 and the input unit 2 are configured independently of each other, but they may be configured integrally like a touch panel. In the present disclosure, the information processing system 100 does not include the display unit 3 or the input unit 2, but may include these.

[0065] The input unit 2 receives input of first information related to a plurality of polyhedrons. The first information may include, for example, the type of polyhedron, the number of polyhedrons, the allowable skewness, the allowable symmetry, etc. Details of the first information and the input of the first information by the input unit 2 will be described later.

[0066] The display control unit 30 causes the display unit 3 to display images and the like based on information output from the output unit 13 of the information processing system 100 .

[0067] The display unit 3 displays images and the like under the control of the display control unit 30. The display unit 3 is, for example, a liquid crystal display, a plasma display, an organic EL (Electro-Luminescence) display, or the like, but is not limited to these.

[0068] The first storage unit 4 is a recording medium for storing the polyhedron database. The recording medium may be, for example, a hard disk drive, a random access memory (RAM), a read-only memory (ROM), or a semiconductor memory. Such a recording medium may be volatile or non-volatile. The polyhedron database includes data related to the polyhedron, such as a diagram of the polyhedron, the number of vertices, the number of edges, the number of faces, or the shape of the faces. Examples of polyhedrons stored in the polyhedron database include regular polyhedrons such as a regular tetrahedron, a regular hexahedron, a regular octahedron, a regular dodecahedron, and a regular icosahedron. Examples of polyhedra include semiregular polyhedra such as a truncated tetrahedron, truncated hexahedron, truncated octahedron, truncated dodecahedron, truncated icosahedron, cuboctahedron, icosidodecahedron, rhombic cuboctahedron, rhombic icosidodecahedron, rhombic truncated cuboctahedron, rhombic truncated icosidodecahedron, modified cube, and modified dodecahedron. The polyhedron data is used when the user inputs the first information via input unit 2.

[0069] Fig. 6 is a diagram showing an example of polyhedron data stored in the first storage unit 4. Fig. 6(a) shows the structure of a polyhedron (here, a regular octahedron), and Fig. 6(b) shows data in which the structure of the polyhedron shown in Fig. 6(a) is described in a predetermined description format (here, xyz file format). For example, an image showing the structure of a polyhedron as shown in Fig. 6(a) and data described in the predetermined description format as shown in Fig. 6(b) are stored as polyhedron data in the first storage unit 4.

[0070] The second storage unit 5 is a recording medium for storing second information related to the three-dimensional structure generated by the generation unit 12. The recording medium is, for example, a hard disk drive, a RAM (Random Access Memory), a ROM (Read Only Memory), or a semiconductor memory. Note that such a recording medium may be volatile or non-volatile.

[0071] FIG. 7 is a diagram showing an example of the second information stored in the second storage unit 5. FIG. 7(a) shows a three-dimensional structure (here, an FCC-type structure) indicated by the second information, and FIG. 7(b) shows data in which the three-dimensional structure shown in FIG. 7(a) is described in a predetermined description format (here, D-Symbol format). The second storage unit 5 stores, as the second information, an image showing the three-dimensional structure as shown in FIG. 7(a) and data described in the predetermined description format as shown in FIG. 7(b). The second information includes, for example, three-dimensional data, graph data, space group, Wyckoff label, cell size, coordinates, or maximum distortion of a polyhedron.

[0072] The file formats (extensions) of the data stored in the second storage unit 5 are, for example, *.sldprt, *.sldasm, *.iam, *.ipt, *.model, *.CATPart, *.CATProduct, *.3ds, or *.max. For information about file formats (extensions), please refer to the site indicated by the URL "https: / / www.data-henkan.com / extension-list".

[0073] The acquisition unit 11 acquires first information about a plurality of polyhedrons, including two or more types of polyhedrons having different shapes. The acquisition unit 11 is an entity that executes the step of acquiring the first information in the information processing method disclosed herein. Specifically, the acquisition unit 11 acquires the first information input by the user via the input unit 2. As will be described later, the user performs an operation to input the first information while viewing a first image displayed on the display unit 3 that accepts input of the first information.

[0074] The generation unit 12 generates second information regarding a three-dimensional structure in which a plurality of polyhedrons are arranged, based on the first information acquired by the acquisition unit 11. The generation unit 12 is an entity that executes the step of generating second information in the information processing method of the present disclosure. In the first embodiment, the generation unit 12 executes a process of converting the acquired first information into a plurality of first number sequences each representing a plurality of polyhedrons, and a process of converting a second number sequence representing a polyhedron generated using the converted first number sequences into a three-dimensional structure. That is, the generation unit 12 executes a process of converting each of the plurality of polyhedrons into a polyhedron code (first number sequence), and a process of converting a polyhedron code (second number sequence) generated using the plurality of polyhedron codes into a three-dimensional structure. Details of each of the above processes will be described later.

[0075] The output unit 13 outputs images, etc. to the display control unit 30, thereby displaying the images, etc. on the display unit 3. The output unit 13 also outputs the second information generated by the generation unit 12. The output unit 13 is the entity that executes the step of outputting the second information in the information processing method of the present disclosure. Specifically, the output unit 13 outputs the second information by displaying a second image representing the second information generated by the generation unit 12 on the display unit 3. As will be described later, the user performs an operation to select the second information to be stored in the second memory unit 5 while looking at the second image displayed on the display unit 3.

[0076] [Use Examples] The following are use examples of the information processing system 100 according to embodiment 1. The information processing system 100 may apply any one of the first to fifth use examples shown below, or may apply a combination of multiple use examples. In the following description of the second to fifth use examples, a description of points common to the first use example will be omitted.

[0077] 8 and 9 are diagrams showing images displayed on the display unit 3 in the first use example of embodiment 1. (a) of Fig. 8 shows an example of a first image displayed on the display unit 3. The first image is displayed on the display unit 3 by the output unit 13 by reading out the polyhedron data stored in the first storage unit 4.

[0078] In the first use example, the first image includes a shape selection area for selecting the shape of a polyhedron, a unit structure selection area for selecting a unit structure (here, a Bravais lattice), and an execution icon called "Generate 3D structure."

[0079] The shape selection area displays multiple polyhedrons selectable by the user and multiple selection buttons corresponding to each of the multiple polyhedrons. The shape selection area may also display the name of each polyhedron's shape. Furthermore, the polyhedrons may be displayed as moving images rather than still images. The user selects a polyhedron to be included in the three-dimensional structure in the shape selection area. As a result, the acquisition unit 11 (in the step of acquiring first information) acquires shape information indicating the shape of each of the multiple polyhedrons as the first information. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a three-dimensional structure in which multiple polyhedrons having the shape indicated by the shape information are arranged without gaps. In the example shown in FIG. 8A, the user selects a regular tetrahedron and a regular octahedron. Therefore, in this case, the generation unit 12 generates second information regarding a three-dimensional structure in which the regular tetrahedron and the regular octahedron are arranged without gaps.

[0080] It is also possible to increase the number of selectable polyhedrons by, for example, paying a fee to the business operator that operates the information processing system 100. In the example shown in Fig. 8(a) , in the column in the shape selection area marked "Available with optional purchase," new selectable polyhedrons are displayed by paying a fee to the user.

[0081] The unit structure selection area displays the types of unit structures (here, Bravais lattices) that the user can select. In the example shown in Fig. 8(a), the user can select either "cubic" or "tetragonal," but the user may also be able to select one from a list of Bravais lattices shown in Fig. 10, for example. Fig. 10 is a diagram showing a list of Bravais lattices.

[0082] The user selects a unit structure (here, a Bravais lattice) in the unit structure selection area. As a result, the acquisition unit 11 (in the step of acquiring first information) acquires, as the first information, unit structure information indicating the shape of a unit structure in which multiple polyhedrons are arranged without gaps. Here, the unit structure information is information indicating a Bravais lattice in a crystal structure. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a three-dimensional structure in which at least one unit structure (here, a Bravais lattice) indicated by the unit structure information is arranged.

[0083] 8B shows an example of the second image displayed on the display unit 3. The second image is displayed on the display unit 3 after the user selects the execution icon in the first image and the generation unit 12 generates second information related to the three-dimensional structure. The second image includes a table showing a list of the three-dimensional structures generated by the generation unit 12 and an execution icon labeled "Export selected three-dimensional structure." The table displays, from left to right, a column for selecting the three-dimensional structure to export, a column displaying an identification number (ID) for each three-dimensional structure, a column indicating the number of each shape of multiple polyhedra included in the three-dimensional structure (here, the composition ratio), and a column indicating the symmetry of the three-dimensional structure (here, the space group).

[0084] The user selects the three-dimensional structure to be saved and selects the execution icon. As a result, an image including an area showing the selected three-dimensional structure and an execution icon labeled "Save Image" is displayed on the display unit 3, as shown in FIG. 9A. The user then confirms the selected three-dimensional structure and, if there are no problems, selects the execution icon. As shown in FIG. 9B, an image including a selection area for selecting a saving format for the three-dimensional structure and an execution icon labeled "Save" is displayed on the display unit 3. Note that in the example shown in FIG. 9B, the user can select either ".slbprt" or ".slbasm," but other saving formats may also be selectable. When the user selects the desired saving format and selects the execution icon, second information regarding the three-dimensional structure selected by the user is saved in the second storage unit 5.

[0085] Fig. 11 is a diagram showing an image displayed on the display unit 3 in a second use example of embodiment 1. Fig. 11 shows an example of a first image displayed on the display unit 3. In the second use example, the first image differs from the first use example in that it includes a symmetry designation area for designating the symmetry of the three-dimensional structure (here, the space group) instead of the unit structure selection area.

[0086] The symmetry specification area displays a text box for the user to specify the desired symmetry of the three-dimensional structure (here, the space group). The space group is used to describe the symmetry of the three-dimensional structure. FIG. 12 is a diagram showing an example of the symmetry of a three-dimensional structure. The three-dimensional structure shown in FIG. 12(a) has the symmetry indicated by the space group "Fm3-m" with the space group number "225". The three-dimensional structure shown in FIG. 12(b) has the symmetry indicated by the space group "l4 / mmm" with the space group number "139". For information about space groups, please refer to the site indicated by the URL "https: / / en.wikipedia.org / wiki / List_of_space_groups".

[0087] The user specifies the symmetry of the three-dimensional structure by inputting the number of the desired space group into the text box in the symmetry specification area. A range of desired space group numbers may also be input into the text box. As a result, the acquisition unit 11 (in the step of acquiring first information) acquires symmetry information indicating the symmetry of the three-dimensional structure as the first information. Here, the symmetry information is information indicating the space group in the crystal structure. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding the three-dimensional structure having the symmetry (here, the space group) indicated by the symmetry information.

[0088] In the second use example, the symmetry designation area of ​​the first image may include a list of space groups that the user can select from, instead of a text box. In this case, the user need only select one of the space groups.

[0089] Fig. 13 is a diagram showing an image displayed on the display unit 3 in a third use example of embodiment 1. Fig. 13 shows an example of a first image displayed on the display unit 3. In the third use example, the first image differs from the first use example in that, instead of a unit structure selection area, the first image includes a number designation area for designating the number of multiple polyhedrons included in the three-dimensional structure for each shape of the polyhedron.

[0090] The number specification area displays the name of the polyhedron shape selected in the shape selection area and a text box for specifying the number of polyhedrons to be included in the three-dimensional structure. In the example shown in Figure 13, the user has selected a regular tetrahedron and a regular octahedron in the shape selection area. Therefore, the number specification area displays a text box for specifying the number of regular tetrahedrons and a text box for specifying the number of regular octahedrons.

[0091] The user specifies the number of polyhedrons to be included in the three-dimensional structure by inputting a desired number in the text box in the number specification area. As a result, the acquisition unit 11 (in the step of acquiring first information) further acquires, as the first information, number information indicating the number of polyhedrons for each shape. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a three-dimensional structure in which multiple polyhedrons of the shape indicated by the shape information are arranged without gaps, in the number of each shape indicated by the number information.

[0092] Fig. 14 is a diagram showing an image displayed on the display unit 3 in a fourth use example of embodiment 1. Fig. 14 shows an example of a first image displayed on the display unit 3. In the fourth use example, the first image differs from the first use example in that it includes a composition ratio designation area for designating a composition ratio for each shape of a polyhedron included in the three-dimensional structure, instead of a unit feature selection area.

[0093] The composition ratio designation area displays the name of the shape of the polyhedron selected in the shape selection area and text boxes for specifying the composition ratio of the polyhedron to be included in the three-dimensional structure. In the example shown in Figure 14, the user has selected a regular tetrahedron and a regular octahedron in the shape selection area. Therefore, the composition ratio designation area displays a text box for specifying the composition ratio of the regular tetrahedron and a text box for specifying the composition ratio of the regular octahedron.

[0094] The user specifies the composition ratio for each shape of the multiple polyhedrons to be included in the three-dimensional structure by inputting a desired composition ratio into a text box in the composition ratio specification area. As a result, the acquisition unit 11 (in the step of acquiring first information) further acquires composition ratio information indicating the composition ratio for each shape of the multiple polyhedrons as the first information. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a three-dimensional structure in which multiple polyhedrons of the shapes indicated by the shape information are arranged without gaps at the composition ratio for each shape indicated by the composition ratio information.

[0095] 15 is a diagram showing an image displayed on the display unit 3 in a fifth use example of embodiment 1. (a) of Fig. 15 shows an example of a first image displayed on the display unit 3. In the fifth use example, unlike the third use example, the first image includes a distortion designation area for designating the allowable distortion of the shapes of multiple polyhedrons.

[0096] Here, the distortion degree indicates the degree to which the shape of the polyhedron indicated by the shape information, i.e., the shape of the polyhedron displayed in the shape selection area, is distorted. For example, the distortion degree is determined based on at least one of the position of the center of gravity of the polyhedron, the position of at least one vertex of the polyhedron, the length of at least one side of the polyhedron, the angle between at least two sides of the polyhedron, and the area of ​​at least one face of the polyhedron, with the shape of the polyhedron indicated by the shape information as the reference.

[0097] For example, when combining polyhedrons of a shape indicated by the shape information, it may be impossible to arrange the polyhedrons without gaps. In such cases, it is possible to arrange the polyhedrons without gaps by distorting the shape of at least one of the polyhedrons. Therefore, in the fifth use example, the generator 12 attempts to generate a three-dimensional structure within the range of distortion acceptable to the user.

[0098] The skewness is expressed by the following formula (1) using, for example, Baur's method. In formula (1), "D" represents the skewness, "l ｉ " is the distance from the center of the polyhedron to the i-th vertex, "l ａｖ " indicates the average distance from the center of the polyhedron to the vertices.

[0099]

[0100] The skewness is expressed by the following formula (2) using, for example, Robinson's method (quadratic elongation). In formula (2), "λ" is the skewness, and "l ｉ " is the distance from the center of the polyhedron to the i-th vertex, "l ０ " indicates the distance from the center to a vertex of a regular polyhedron of the same volume.

[0101]

[0102] FIG. 16 is a diagram showing an example of the distortion of a polyhedron. FIG. 16(a) shows the case where the distortion "D" is "0.0", that is, the shape of a polyhedron (here, a regular tetrahedron) without distortion. On the other hand, FIG. 16(b) shows the case where the distortion "D" is "0.00869", that is, the shape of a polyhedron (here, a regular tetrahedron) with distortion. FIG. 17 is a diagram showing an example of a three-dimensional structure with distortion. FIG. 17 shows a three-dimensional structure (here, a BCC structure) in which multiple distorted polyhedrons (here, polyhedrons obtained by distorting regular tetrahedrons) are arranged without gaps.

[0103] The distortion specification area displays a text box for specifying the allowable distortion of the shapes of the multiple polyhedrons. The user specifies the allowable distortion of the shapes of the multiple polyhedrons by inputting a desired distortion into the text box in the distortion specification area. Note that a desired range of distortion may also be input into the text box. As a result, the acquisition unit 11 (in the step of acquiring first information) further acquires distortion information indicating the allowable distortion of the shapes of the multiple polyhedrons as the first information. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a three-dimensional structure in which at least a portion of the multiple polyhedrons is distorted so as not to exceed the distortion indicated by the distortion information.

[0104] 15(b) shows an example of the second image displayed on the display unit 3. In the fifth use example, unlike the first use example, the second image further includes a column displaying total strain, which is the sum of the strains of the three-dimensional structures, in the table showing the list of three-dimensional structures generated by the generation unit 12.

[0105] [Operation] The following describes the operation (that is, the information processing method) of the information processing system 100 according to Embodiment 1. Fig. 18 is a flowchart showing an example of the operation of the information processing system 100 according to Embodiment 1.

[0106] (Step S101) The acquisition unit 11 acquires first information. As described above, the first information is acquired by the acquisition unit 11 when the user reads out the polyhedron data stored in the first storage unit 4 and inputs (selects) the first information using the input unit 2 while viewing the first image displayed on the display unit 3. Note that the first information may also be acquired by the acquisition unit 11 when the user inputs original data using the input unit 2 without referring to the first image.

[0107] (Step S102) The generation unit 12 executes a process of converting the first information acquired by the acquisition unit 11 into a plurality of first number sequences each representing a plurality of polyhedrons. Here, the generation unit 12 converts each polyhedron included in the first information into a polyhedron code.

[0108] (Step S103) The generator 12 executes a process of generating a second number sequence representing a polyhedron using the converted first number sequences. Here, the generator 12 generates a plurality of polyhedron codes based on the plurality of polyhedron codes obtained by the conversion.

[0109] (Step S104) The generation unit 12 determines whether the generated polyhedron code can be converted into a three-dimensional structure. The generation unit 12 can determine whether the polyhedron code can be converted into a three-dimensional structure based on, for example, whether the faces of two adjacent polyhedrons are the same, and whether multiple polyhedrons are arranged without gaps (in other words, whether the filling rate is 100%). If it is determined that conversion is possible (Step S104: Yes), the generation unit 12 then executes Step S105. If it is determined that conversion is not possible (Step S104: No), the generation unit 12 then executes Step S106.

[0110] (Step S105) The generator 12 executes a process of converting the polyhedron code into a three-dimensional structure. For the conversion process, for example, the method of K. Nishio et al. or the method of O. Delgado-Friedrichs et al. can be used. The generator 12 then executes step S106.

[0111] (Step S106) The generation unit 12 determines whether there are any polyhedra codes for which it has not yet determined whether they are convertible. If there are any polyhedra codes for which it has not yet determined whether they are convertible (S106: Yes), the generation unit 12 returns to step S104. If it has determined all polyhedra codes (S106: No), the processing by the generation unit 12 is completed. Then, the information processing system 100 (information processing method) next executes step S107.

[0112] (Step S107) The output unit 13 executes a process of outputting the second information generated by the generation unit 12. Here, the output unit 13 outputs the second information by causing the display unit 3 to display a second image representing the second information generated by the generation unit 12.

[0113] The display unit 3 may include a display control unit 30. The display unit 3 including the display control unit 30 may be referred to as a display unit 3A. The output unit 13 may output the second information generated by the generation unit 12 to the display unit 3A. As a result, the display unit 3A may display the second information. In other words, the output unit 13 may cause the display unit 3A to display the second information.

[0114] If the generating unit 12 cannot convert all of the polyhedral codes into a three-dimensional structure, the second information is not generated. If the generating unit 12 cannot convert all of the polyhedral codes into a three-dimensional structure, the second information is not displayed on the display unit 3.

[0115] Next, the process of converting a polyhedron into a polyhedron code will be specifically described with reference to the drawings. Figure 19 is a flowchart showing an example of the process of generating a polyhedron code from a polyhedron.

[0116] (Step S201) The generating unit 12 assigns the number "1" to any face of the polyhedron.

[0117] (Step S202) The generation unit 12 assigns “1” to the variable “i”.

[0118] (Step S203) The generation unit 12 assigns the number "i+1" to the face adjacent to the "i"-th face.

[0119] (Step S204) The generation unit 12 assigns numbers to the variable "j" number of faces adjacent to the "i"-th face, starting from the "i+1"-th face clockwise to the "i+j"-th face. The variable "j" is assigned the number of faces adjacent to the "i"-th face.

[0120] (Step S205) The generation unit 12 determines whether numbers have been assigned to all faces of the polyhedron. If numbers have been assigned to all faces of the polyhedron (Step S205: Yes), the generation unit 12 then executes Step S209. If numbers have not yet been assigned to all faces of the polyhedron (Step S205: No), the generation unit 12 then executes Step S206.

[0121] (Step S206) The generation unit 12 assigns the number "i+j+1" to an unnumbered face adjacent to the face numbered "i+1".

[0122] (Step S207) The generation unit 12 determines whether numbers have been assigned to all faces of the polyhedron. If numbers have been assigned to all faces of the polyhedron (Step S207: Yes), the generation unit 12 then executes Step S209. If numbers have not yet been assigned to all faces of the polyhedron (Step S207: No), the generation unit 12 then executes Step S208.

[0123] (Step S208) The generation unit 12 assigns "i+j" to the variable "i." Then, the generation unit 12 returns to step S204.

[0124] (Step S209) The generating unit 12 arranges the numbers of sides of each face in the order of the numbers assigned to all faces of the polyhedron, thereby creating a sequence of the numbers of sides of each face.

[0125] (Step S210) The generation unit 12 determines whether or not there are other number sequence patterns. If there are other number sequence patterns (Step S210: Yes), the generation unit 12 returns to Step S201. In this case, in Step S201, the generation unit 12 assigns the number "1" to any face different from the face to which the number "1" was previously assigned. If there are no other number sequence patterns (Step S210: No), the generation unit 12 then executes Step S211.

[0126] (Step S211) The generation unit 12 selects the smallest number sequence from one or more number sequences. The selected number sequence becomes the polyhedron code.

[0127] Below, specific examples of the process of converting a polyhedron into a polyhedron code are listed.

[0128] 20 shows an example of the process of generating a polyhedron code from a regular tetrahedron. First, the generator 12 assigns the number "1" to an arbitrary face. Then, the generator 12 assigns the numbers "2," "3," and "4" to the faces adjacent to the face "1" in a clockwise (left-handed) direction.

[0129] In FIG. 20, the face numbered "1" is １ , the face assigned the number "2" is ２ , the face assigned the number "3" is ３ , the face assigned the number "4" is ４ Let's say. １ is the right front face of each regular tetrahedron shown in FIG. １ The three sides of the tetrahedron are named clockwise as side a, side b, and side c. １ FIG. 49 shows the sides a, b, and c of the regular tetrahedron. １ In FIG. １ is filled in black. ２ is face １ and share edge a, and face ３ is face １ and share edge b, and face ４ is face １ and share edge c.

[0130] As a result, numbers are assigned to all faces, and the generation unit 12 generates a sequence in numerical order, with the number of sides of the face as a term. In other words, if a face is a triangle, it has three sides, so the term corresponding to that face is "3". Therefore, the sequence representing each face of a regular tetrahedron is "3333 = 3" in the order of numbers from "1" to "4". ４ In this case, since there is no other pattern of the sequence, the regular tetrahedron has the polyhedron code "3 ４ " is converted to

[0131] FIG. 21 illustrates an example of a process for generating a polyhedron code from a regular octahedron. First, the generation unit 12 assigns the number "1" to an arbitrary face. Then, the generation unit 12 assigns the numbers "2," "3," and "4" to faces adjacent to the face "1" in a clockwise (left-handed) direction. Next, the generation unit 12 assigns the number "5" to a face adjacent to the face "2" that has not yet been assigned a number. Then, the generation unit 12 assigns the numbers "6" and "7" to faces adjacent to faces numbered "4" or lower in a clockwise (left-handed) direction, starting from the face "5." Finally, the generation unit 12 assigns the number "8" to a face adjacent to the face "5" that has not yet been assigned a number.

[0132] In FIG. 21, the face numbered "1" is １ ,~,the face assigned the number "8" ８ Let's say. １ is the far right face of each regular octahedron shown in Figure 21. １ The three sides of the octahedron are named a, b, and c in clockwise order. １ 1 is a diagram showing sides a, b, and c of the face ２ is face １ and share edge a, and face ３ is face １ and share edge b, and face ４ is face １ The face of the regular octahedron is ２ In FIG. ２ are filled in black. Figure 52 shows the faces of a regular octahedron. ５ In FIG. ５ are filled in black. Figure 53 shows the faces of a regular octahedron. ６ In FIG. ６ is filled in black.

[0133] As a result, numbers are assigned to all faces, and the generation unit 12 generates a sequence in numerical order, with the number of sides of the face as a term. In other words, if a face is a triangle, it has three sides, so the term corresponding to that face is "3". Therefore, the sequence representing each face of a regular octahedron is "33333333 = 3" in the order of numbers from "1" to "8". ８In this case, since there is no other pattern of the sequence, the regular octahedron has the polyhedron code "3 ８ " is converted to

[0134] FIG. 22 illustrates an example of a process for generating a polyhedron code from a cuboctahedron. First, the generation unit 12 assigns the number "1" to an arbitrary face. Then, the generation unit 12 assigns the numbers "2," "3," and "4" to faces adjacent to the face "1" in a clockwise (left-handed) direction, in order. Next, the generation unit 12 assigns the number "5" to a face adjacent to the face "2" that has not yet been assigned a number. Then, the generation unit 12 assigns the numbers "6," "7," "8," "9," and "10" to faces adjacent to faces numbered "4" or lower in a clockwise (left-handed) direction, starting from the face "5." Furthermore, the generation unit 12 assigns the number "11" to a face adjacent to the face "5" that has not yet been assigned a number. Then, the generation unit 12 assigns the numbers "12" and "13" to faces adjacent to faces numbered "10" or lower in a clockwise (left-handed) direction, starting from the face "11." Furthermore, the generation unit 12 assigns the number "14" to a face adjacent to the face "11" and to which no number has yet been assigned.

[0135] In FIG. 22, the face numbered "1" is １ , ... １４ Let's say. １ is the triangular face at the far right of each cuboctahedron shown in Figure 22. １ The three sides of the cuboctahedron are named a, b, and c in clockwise order. １ 1 is a diagram showing sides a, b, and c of the face ２ is face １ and share edge a, and face ３ is face １ and share edge b, and face ４ is face １ The face of the cuboctahedron is ２ In FIG. ２ are filled in black. Figure 56 shows the faces of a cuboctahedron. ６ In FIG. ６are filled in black. Figure 57 shows the faces of a cuboctahedron. ７ In FIG. ７ is filled in black.

[0136] As a result, numbers are assigned to all faces, and the generation unit 12 generates a sequence in numerical order, with the number of sides of the face as a term. That is, if the face is a triangle, it has three sides, so the term corresponding to that face is "3." If the face is a square, it has four sides, so the term corresponding to that face is "4." Therefore, the sequence representing each face of the cuboctahedron is "344433333334443 = 34" in the order of numbers from "1" to "14." ３ 3 ６ 4 ３ In this case, the sequence is the smallest sequence compared to other sequence patterns, so the cuboctahedron has the polyhedron code "34". ３ 3 ６ 4 ３ is converted to "3".

[0137] If integer A is less than integer B, then sequence A is less than sequence B. In the cuboctahedron example above, if you first select the triangle, the result is "344433333334443 = 34 ３ 3 ６ 4 ３ If you select a square, you get a sequence of 3, but if you select a square, you get 43333444433334 = 43 ４ 4 ４ 3 ４ A sequence of "4" is obtained. In other words, since one polyhedron has multiple sequence of numbers, it is necessary to uniquely determine the sequence. As an example, the smallest sequence can be selected. In this case, the sequence 43333444433334 is larger than the sequence 34443333334443, so the sequence 344433333334443 is selected.

[0138] The process of generating a plurality of polyhedron codes based on a plurality of polyhedron codes will be specifically described below with reference to the accompanying drawings. Fig. 23 is a flowchart showing an example of the process of generating a polyhedron code from a polyhedron code. Here, the description will be given assuming that the acquiring unit 11 acquires the shape of each of the plurality of polyhedrons and the number of each shape as the first information.

[0139] (Step S301) The generating unit 12 acquires the shape of each of the multiple polyhedrons and the number of each shape from the first information acquired by the acquiring unit 11.

[0140] (Step S302) The generating unit 12 converts each of the plurality of polyhedrons into a polyhedron code, thereby preparing a plurality of polyhedron codes.

[0141] (Step S303) The generating unit 12 generates a plurality of polyhedron codes based on the plurality of polyhedron codes.

[0142] For example, suppose that the polyhedrons consist of eight regular tetrahedrons and four regular octahedrons. In this case, the polyhedron code "3" corresponding to the regular tetrahedrons is ４ " is "T=3 ４ ", the polyhedron code corresponding to the regular octahedron "3 ８ " is "O=3 ８ Therefore, in step S303, the generating unit 12 generates a plurality of polyhedron codes by rearranging the sequence "OOOOTTTTTTTT" of the plurality of polyhedron codes. For example, the polyhedron code is expressed as "TOOOOTTTTTTT=TO ４ T ７ That is, in step S303, a plurality of polyhedron codes are generated based on the plurality of polyhedron codes, i.e., eight Ts and four Os. Each of the plurality of polyhedron codes includes eight Ts and four Os. "OOOOTTTTTTTT" and "TOOOOOTTTTTTTT" are different polyhedron codes.

[0143] The process of converting a polyhedral code into a three-dimensional structure will be specifically described below with reference to the accompanying drawings. The process described below also includes a process of determining whether the polyhedral code can be converted into a three-dimensional structure. Figure 24 is a flowchart showing an example of the process of generating a three-dimensional structure from a polyhedral code.

[0144] (Step S401) The generation unit 12 generates each term of the polyhedron code, that is, a polyhedron corresponding to the polyhedron code.

[0145] (Step S402) The generation unit 12 assigns numbers to each face of the polyhedron clockwise in the order of the terms of the polyhedron code. For example, if numbers "1" to "4" are assigned to the polyhedron corresponding to the first term of the polyhedron code, numbers starting from "5" are assigned to the polyhedron corresponding to the second term of the polyhedron code. In other words, the generation unit 12 assigns numbers to each face of each polyhedron so that numbers do not overlap among the polyhedrons.

[0146] (Step S403) The generating unit 12 determines the polyhedron having the unconnected face with the smallest number as the partial polyhedron.

[0147] (Step S404) The generation unit 12 selects a face of the remaining polyhedron having the same shape as the face with the smallest number of the partial polyhedron. For example, if the face with the smallest number of the partial polyhedron has a triangular shape, the generation unit 12 selects a face with the same triangular shape from the remaining polyhedron. Here, one face may be selected, or multiple faces may be selected.

[0148] (Step S405) The generating unit 12 connects the face with the smallest number among the selected faces to the unconnected face with the smallest number of the partial polyhedron.

[0149] (Step S406) The generation unit 12 determines whether there is an unconnected pair of faces between the faces of the partial polyhedron and the faces of the selected remaining polyhedron. If there is an unconnected pair of faces (Step S406: Yes), the generation unit 12 then executes Step S407. If there is no unconnected pair of faces (Step S406: No), the generation unit 12 then executes Step S408.

[0150] (Step S407) The generation unit 12 connects the unconnected faces of the partial polyhedron and the selected remaining polyhedron, and then returns to step S406.

[0151] (Step S408) The generation unit 12 determines whether or not there are any remaining unconnected polyhedrons. If there are any remaining unconnected polyhedrons (Step S408: Yes), the generation unit 12 returns to Step S403. If there are no remaining unconnected polyhedrons (Step S408: No), the generation unit 12 then executes Step S409.

[0152] (Step S409) The generation unit 12 determines whether all polyhedrons are 100% filled, in other words, whether all polyhedrons are arranged without gaps. If all polyhedrons are 100% filled (step S409: Yes), the processing of the generation unit 12 is completed. In this case, the generation unit 12 has converted the polyhedron code into a three-dimensional structure. If all polyhedrons are not 100% filled (step S409: No), the generation unit 12 next executes step S410.

[0153] (Step S410) The generator 12 discards the three-dimensional structure whose filling rate is not 100% and completes the process. In this case, the generator 12 does not convert the polyhedron code into a three-dimensional structure.

[0154] A specific example of the process of converting a polyhedral code into a three-dimensional structure will be described below with reference to the drawings. Fig. 25 is a diagram showing a specific example of a polyhedral code. Fig. 26 is a diagram showing a specific example of the process of generating a three-dimensional structure from a polyhedral code. As shown in Fig. 25, the following describes the case where the polyhedral code "TOOOOTTTTTTT" is converted into a three-dimensional structure.

[0155] First, the generation unit 12 converts the polyhedron codes "T" and "O" in the polyhedron code into the corresponding polyhedrons. In this case, the polyhedron code "T" is a regular tetrahedron, and the polyhedron code "O" is a regular octahedron. Next, the generation unit 12 assigns numbers to each face of the polyhedron clockwise in the order of the multiple terms included in the polyhedron code. For example, the faces of the regular tetrahedron corresponding to the first term (the leftmost term) of the polyhedron code are assigned numbers "1" to "4," and the faces of the regular octahedron corresponding to the second term are assigned numbers "5" to "10." Then, the generation unit 12 determines the regular tetrahedron corresponding to the first term of the polyhedron code as a partial polyhedron.

[0156] Next, the generation unit 12 selects the faces of the remaining polyhedra that have the shape of the face with the lowest number of the regular tetrahedron, which is the partial polyhedron. In this case, the shape of the face with the lowest number of the partial polyhedron, "1," is triangular, and the faces of all the remaining polyhedrons are also triangular, so the faces of all the remaining polyhedrons are selected. Thereafter, the generation unit 12 combines the face with the lowest number of the selected faces with the uncombined face with the lowest number of the partial polyhedron. In this case, the face with the number "1" of the regular tetrahedron, which is the partial polyhedron, is combined with the face with the number "5" of the regular octahedron, which corresponds to the second term in the polyhedron code.

[0157] Next, since there are pairs of unconnected faces between the faces of the partial polyhedron and the faces of the selected remaining polyhedron, the generation unit 12 repeats the process of connecting the unconnected faces. Here, the generation unit 12 connects the unconnected face with the smallest number "2" of the partial polyhedron to the unconnected face with the smallest number "13" of the selected remaining polyhedron. In the same manner, the generation unit 12 connects the face "3" to the face "21" and the face "4" to the face "29".

[0158] Next, since there are remaining unconnected polyhedra, the generation unit 12 determines the polyhedron with the smallest unconnected face number among the remaining polyhedra (here, the regular octahedron corresponding to the second term in the polyhedron code) as the new partial polyhedron, and repeats the same process as above.

[0159] The generation unit 12 then repeats the above process until there are no remaining unconnected polyhedra, thereby generating a three-dimensional structure with a filling rate of 100%. That is, the generation unit 12 connects the unconnected face "6" of the new partial polyhedron, which is the smallest unconnected face of the selected remaining polyhedron, with the unconnected face "37" of the smallest unconnected face of the selected remaining polyhedron. Similarly, the generation unit 12 connects the face "7" with the face "41," the face "8" with the face "45," the face "9" with the face "49," the face "10" with the face "53," the face "11" with the face "57," and the face "12" with the face "59." In the case of the polyhedron code "TOOOTTTTTTTT," the three-dimensional structure generated by the generation unit 12 is an fcc-type structure.

[0160] An example of the operation of the information processing system 100 according to the first embodiment, the display unit 3, the first storage unit 4, and the second storage unit 5 will be described below with reference to the drawings. Fig. 27 is a sequence diagram showing an example of the operation of the information processing system 100 according to the first embodiment, the display unit 3, the first storage unit 4, and the second storage unit 5.

[0161] (Step S501) The acquisition unit 11 of the information processing system 100 acquires first information. Here, the first information is acquired by the acquisition unit 11 when the user reads out the polyhedron data stored in the first storage unit 4 and inputs (selects) the first information using the input unit 2 while viewing the first image displayed on the display unit 3.

[0162] (Step S502) The generating unit 12 of the information processing system 100 executes a process of converting each polyhedron included in the first information acquired by the acquiring unit 11 into a polyhedron code.

[0163] (Step S503) The generating unit 12 of the information processing system 100 executes a process of generating a plurality of polyhedron codes based on the plurality of polyhedron codes obtained by the conversion.

[0164] (Step S504) The generation unit 12 of the information processing system 100 executes a process of determining whether the generated polyhedral code can be converted into a three-dimensional structure.

[0165] (Step S505) The generating unit 12 of the information processing system 100 executes a process of converting the polyhedron code determined to be convertible into a three-dimensional structure.

[0166] (Step S506 ) The display unit 3 displays the second image representing the second information output from the output unit 13 of the information processing system 100 .

[0167] (Step S507) When the user selects a three-dimensional structure to be saved while viewing the second image displayed on the display unit 3, the information processing system 100 provides second information related to the selected three-dimensional structure to the second storage unit 5. As a result, the second storage unit 5 saves the second information related to the three-dimensional structure selected by the user.

[0168] As described above, in the first embodiment, by inputting information on a plurality of polyhedrons, including two or more types of polyhedrons with mutually different shapes, it becomes possible to comprehensively generate a three-dimensional structure (i.e., a space-filling structure in a three-dimensional space) formed by combining the inputted plurality of polyhedrons. Therefore, in the first embodiment, the comprehensively generated three-dimensional structure can be used to search for unknown materials, thereby improving the efficiency of the search for unknown materials.

[0169] Incidentally, in the information processing system 100 (information processing method) according to the first embodiment, a polyhedron is converted into a polyhedron code, a polyhedron code is generated from the converted polyhedron code, and the generated polyhedron code is converted into a three-dimensional structure. However, this is not limited to this. The information processing system 100 according to the first embodiment may also convert a polyhedron into a polyhedron graph, generate a cyclic graph from the converted polyhedron graph, and convert the generated cyclic graph into a three-dimensional structure. That is, the generation unit 12 (the step of generating second information) may execute a process of converting the acquired first information into a plurality of polyhedron graphs each representing a plurality of polyhedra, and a process of converting the cyclic graph generated using the converted polyhedron graphs into a three-dimensional structure.

[0170] The following describes the above operation (that is, the information processing method) of the information processing system 100 according to Embodiment 1. Fig. 28 is a flowchart showing another example of the operation of the information processing system 100 according to Embodiment 1.

[0171] (Step S108) The acquisition unit 11 acquires the first information. As described above, the first information is acquired by the acquisition unit 11 when the user reads out the polyhedron data stored in the first storage unit 4 and inputs (selects) the first information using the input unit 2 while viewing the first image displayed on the display unit 3. Note that the first information may also be acquired by the acquisition unit 11 when the user inputs original data using the input unit 2 without referring to the first image.

[0172] (Step S109) The generating unit 12 determines the positions of the vertices (vertex sites) of each polyhedron and the positions of the centers (center sites) of each polyhedron based on the acquired first information.

[0173] (Step S110) The generation unit 12 executes a process of converting the first information acquired by the acquisition unit 11 into a plurality of polyhedron graphs each representing a plurality of polyhedrons. Here, the generation unit 12 converts each polyhedron included in the first information into a polyhedron graph.

[0174] (Step S111) The generation unit 12 executes a process of generating a cyclic graph using the converted polyhedral graph. Here, the generation unit 12 generates a plurality of cyclic graphs based on a combination of the plurality of polyhedral graphs obtained by the conversion.

[0175] (Step S112) The generation unit 12 determines whether the generated periodic graph can be converted into a three-dimensional structure. The generation unit 12 can determine whether the periodic graph can be converted into a three-dimensional structure based on, for example, whether the faces of two adjacent polyhedrons are the same, and whether multiple polyhedrons are arranged without gaps (in other words, whether the filling rate is 100%). If it is determined that conversion is possible (Step S112: Yes), the generation unit 12 then executes Step S113. If it is determined that conversion is not possible (Step S112: No), the generation unit 12 then executes Step S114.

[0176] (Step S113) The generation unit 12 executes a process of converting the periodic graph into a three-dimensional structure. For the conversion process, for example, the method described in the Kotani-Sunada theory (Kotani-Sunada, 2000, Trans. Amer. Mat.) can be used. The generation unit 12 then executes step S114.

[0177] (Step S114) The generation unit 12 determines whether there are any periodic graphs for which it has not yet been determined whether they can be converted. If there are any periodic graphs for which it has not yet been determined (S114: Yes), the generation unit 12 returns to step S112. If it has determined all periodic graphs (S114: No), the processing by the generation unit 12 is completed. Then, the information processing system 100 (information processing method) next executes step S115.

[0178] (Step S115) The output unit 13 executes a process of outputting the second information generated by the generation unit 12. Here, the output unit 13 outputs the second information by causing the display unit 3 to display a second image representing the second information generated by the generation unit 12.

[0179] The display unit 3 may include a display control unit 30. The display unit 3 including the display control unit 30 may be referred to as a display unit 3A. The output unit 13 may output the second information generated by the generation unit 12 to the display unit 3A. As a result, the display unit 3A may display the second information. In other words, the output unit 13 may cause the display unit 3A to display the second information.

[0180] A specific example of a process for generating a three-dimensional structure from a polyhedron will be described below with reference to the drawings. Fig. 29 shows a specific example of a process for converting a polyhedron into a polyhedron graph. Fig. 30 shows a specific example of converting a cyclic graph into a three-dimensional structure.

[0181] First, the generation unit 12 determines each vertex site of the polyhedron and the central site of the polyhedron. In the case of a regular tetrahedron shown in (a) of Fig. 29, the generation unit 12 determines four vertex sites and one central site as shown in (b) of Fig. 29. In the case of a regular octahedron shown in (d) of Fig. 29, the generation unit 12 determines six vertex sites and one vertex site as shown in (e) of Fig. 29.

[0182] Next, the generation unit 12 generates a polyhedron graph by connecting each vertex site of the polyhedron to the central site. If the polyhedron is a regular tetrahedron, the generation unit 12 generates a polyhedron graph in which edges extend from the central node to each of the four vertex nodes, as shown in (c) of Fig. 29. If the polyhedron is a regular octahedron, the generation unit 12 generates a polyhedron graph in which edges extend from the central node to each of the six vertex nodes, as shown in (f) of Fig. 29.

[0183] Next, the generation unit 12 generates a cyclic graph by connecting each vertex node in the generated polyhedral graph. The cyclic graph shown in (a) of FIG. 30 is generated from two polyhedral graphs corresponding to two regular tetrahedrons and one polyhedral graph corresponding to one regular octahedron. This cyclic graph is generated by connecting the vertex nodes of each polyhedral graph together. Then, the generation unit 12 converts the generated cyclic graph into a three-dimensional structure. The three-dimensional structure (FCC type structure) shown in (b) of FIG. 30 is generated by converting the cyclic graph shown in (a) of FIG. 30.

[0184] (Embodiment 2) An information processing system 200 (information processing method or program) according to embodiment 2 of the present disclosure will be described in detail below with reference to the drawings. The information processing system 200 according to embodiment 2 differs from the information processing system 100 according to embodiment 1 in that the acquisition unit 11 acquires material information related to the composition of the material as the first information. Note that, like the information processing system 100 according to embodiment 1, the information processing system 200 according to embodiment 2 includes the acquisition unit 11, the generation unit 12, and the output unit 13, and since the configuration is the same, description of these components will be omitted.

[0185] [Examples of Use] The following lists examples of use of the information processing system 200 according to embodiment 2. In the following description of the second example of use, a description of points common to the first example of use will be omitted.

[0186] 31, 32, and 33 are all diagrams showing images displayed on the display unit 3 in the first use example of embodiment 2. (a) of Fig. 31 and (b) of Fig. 31 all show examples of a first image that is initially displayed on the display unit 3. The display unit 3 may display the first image shown in (a) of Fig. 31, or may display the first image shown in (b) of Fig. 31.

[0187] The first image shown in (a) of FIG. 31 includes an element selection area for selecting an element and an execution icon labeled "Next." A periodic table is displayed in the element selection area. The user selects an element (atom) contained in a desired material in the element selection area. For example, if the user performs a selection operation on the same element once, the element becomes the element located at the center of a polyhedron. On the other hand, if the user performs a selection operation on the same element twice, the element becomes the element located at a vertex of the polyhedron. When the user selects the execution icon, the acquisition unit 11 (in the step of acquiring first information) acquires material information regarding the composition of the material (here, the atoms contained in the material) as the first information.

[0188] The first image shown in (b) of FIG. 31 includes a composition specification area for specifying the composition of a material and an execution icon labeled "Next." The composition specification area displays a text box for the user to specify the composition of the material desired. The user inputs the composition formula of the desired material into the text box. When the user selects the execution icon, the acquisition unit 11 (in the step of acquiring first information) acquires material information regarding the composition of the material (here, the composition of the material itself) as the first information. Note that subscripts are omitted from the composition formula shown in (b) of FIG. 31.

[0189] Fig. 32 shows an example of a first image that is displayed second on the display unit 3. The first image shown in Fig. 32 is displayed on the display unit 3 when the user selects the execution icon in the first image shown in Fig. 31 (a) or the first image shown in Fig. 31 (b). The first image shown in Fig. 32 displays an arrangement designation area for designating the arrangement of elements (atoms) contained in the material, and an execution icon labeled "Next." The arrangement designation area displays a table showing the number of each element in the polyhedron and the position (vertex or center) of each element in the polyhedron.

[0190] 32 is displayed on the display unit 3 via the first image shown in FIG. 31(a), the positions of each element have already been specified in the placement designation area. Therefore, the user specifies the number of each element in the polyhedron and selects the execute icon. In this case, the acquisition unit 11 (in the step of acquiring first information) acquires, as the first information, placement information regarding the placement of elements (atoms) in the three-dimensional structure.

[0191] On the other hand, when the first image shown in Figure 32 is displayed on the display unit 3 via the first image shown in Figure 31 (b), the number of each element has already been specified in the placement designation area. Therefore, the user designates the placement of each element in the polyhedron and selects the execution icon. In this case, too, the acquisition unit 11 (in the step of acquiring first information) acquires, as the first information, placement information regarding the placement of elements (atoms) in the three-dimensional structure.

[0192] FIG. 33 shows an example of a first image that is displayed third on the display unit 3. The first image shown in FIG. 33 is displayed on the display unit 3 when the user selects the execution icon in the first image shown in FIG. 32. The first image shown in FIG. 33 includes a combination selection area for selecting a combination of polyhedrons, a distortion specification area, and an execution icon labeled "Generate 3D structure." Note that the first image shown in FIG. 33 may include, for example, a unit structure selection area instead of the distortion specification area. In other words, any one of the first to fifth use examples of embodiment 1, or a combination thereof, may be applied to the first image shown in FIG. 33, excluding the combination selection area.

[0193] The combination selection area displays combinations of multiple polyhedrons that the user can select based on the arrangement information, and multiple selection buttons corresponding to each combination of multiple polyhedrons. The combination selection area may also display the name of the shape of each polyhedron. The combination selection area may also display each polyhedron as a moving image rather than a still image. The user selects a combination of polyhedrons to be included in the three-dimensional structure in the combination selection area. As a result, the acquisition unit 11 (in the step of acquiring first information) acquires, as the first information, shape information indicating the shape of each of the multiple polyhedrons and composition ratio information indicating the composition ratio of each shape.

[0194] When the user selects the execution icon, the following process is executed.

[0195] The generation unit 12 determines number information indicating the number of each of the multiple polyhedron shapes based on the composition ratio information. The number information may be multiple pieces of number information. For example, assume that information indicating a ratio of the number of regular tetrahedrons to the number of regular octahedrons = 2:1 is selected in FIG. 33. The multiple pieces of number information may be information indicating (the number of regular tetrahedrons is 2, the number of regular octahedrons is 1), (the number of regular tetrahedrons is 4, the number of regular octahedrons is 2), ..., (the number of regular tetrahedrons is 2 x n, the number of regular octahedrons is 1 x n). n may be a natural number greater than or equal to 2 and may be a predetermined value. The following processing may be performed for each of the multiple pieces of number information.

[0196] The generation unit 12 (in the step of generating second information) generates second information about a three-dimensional structure in which a plurality of polyhedrons having a shape indicated by the shape information are arranged without gaps in the number corresponding to the polyhedrons. In other words, the generation unit 12 generates second information about a three-dimensional structure in which a plurality of polyhedrons having a shape indicated by the shape information are arranged without gaps at the composition ratio for each shape indicated by the composition ratio information. Here, the shape information and composition ratio information are information based on the arrangement information. Therefore, it can be said that the generation unit 12 (in the step of generating second information) generates second information about a three-dimensional structure based on the arrangement of elements (atoms) indicated by the arrangement information.

[0197] Thereafter, similarly to the first usage example of embodiment 1, a second image is displayed on the display unit 3. Then, the user selects the three-dimensional structure that he or she wishes to save and the format in which the three-dimensional structure is to be saved, and the second information regarding the three-dimensional structure selected by the user is saved in the second storage unit 5.

[0198] Hereinafter, a first operation example of the information processing system 200 according to the second embodiment, and the display unit 3, the first storage unit 4, and the second storage unit 5 will be described with reference to the drawings. Fig. 34 is a sequence diagram showing a first operation example of the entire information processing system 200 according to the second embodiment, including the display unit 3, the first storage unit 4, and the second storage unit 5.

[0199] (Step S601) The acquisition unit 11 of the information processing system 200 acquires material information and placement information. Here, the material information is acquired by the acquisition unit 11 when the user inputs (selects) the material information using the input unit 2 while viewing the first image (see FIG. 31 ) that is displayed first on the display unit 3. Also, the placement information is acquired by the acquisition unit 11 when the user inputs (selects) the material information using the input unit 2 while viewing the first image (see FIG. 32 ) that is displayed second on the display unit 3.

[0200] (Step S602) The acquisition unit 11 of the information processing system 200 searches for a combination of multiple polyhedrons that the user can select based on the arrangement information. When searching for a combination of multiple polyhedrons, the acquisition unit 11 reads and refers to the polyhedron data stored in the first storage unit 4.

[0201] (Step S603) The display unit 3 displays the combinations of the multiple polyhedrons output from the output unit 13 of the information processing system 200. In other words, the display unit 3 displays a first image including a combination selection area for selecting a combination of polyhedrons.

[0202] (Step S604) The acquisition unit 11 of the information processing system 200 acquires the first information. Here, the first information is shape information and composition ratio information, and is acquired by the acquisition unit 11 when the user inputs (selects) the first information using the input unit 2 while viewing the first image (see FIG. 33 ) displayed third on the display unit 3.

[0203] (Step S605) The generation unit 12 of the information processing system 200 executes a process of converting the polyhedron code determined to be convertible into a three-dimensional structure. Note that step S605 is the same process as step S505 (see FIG. 27). Furthermore, between step S604 and step S605, the same processes as steps S502 to S504 (see FIG. 27) are executed.

[0204] (Step S606 ) The display unit 3 displays the second image representing the second information output from the output unit 13 of the information processing system 200 .

[0205] (Step S607) When the user selects a three-dimensional structure to be saved while viewing the second image displayed on the display unit 3, the information processing system 200 provides second information related to the selected three-dimensional structure to the second storage unit 5. As a result, the second storage unit 5 saves the second information related to the three-dimensional structure selected by the user.

[0206] 35 and 36 are both diagrams showing images displayed on the display unit 3 in a second use example of embodiment 2. Fig. 35 shows an example of a first image that is displayed second on the display unit 3. In the second use example, the first image shown in Fig. 35 is displayed on the display unit 3 instead of the first image shown in Fig. 32. The first image shown in Fig. 35 differs from the first image shown in Fig. 32 in that, instead of the execution icon "Next," it includes a first execution icon "Yes" for inputting polyhedron information and an execution icon "No" for not inputting polyhedron information.

[0207] When the user selects the first execution icon in the first image shown in FIG. 35 , the display unit 3 displays a first image (see FIG. 8( a), FIG. 11, FIG. 13, FIG. 14, and FIG. 15( a)) that prompts the user to input polyhedron information, for example, any one of the first to fifth use examples of embodiment 1, or a combination thereof. Therefore, when the user inputs (selects) polyhedron information while viewing the first image displayed on the display unit 3, the acquisition unit 11 (in the step of acquiring first information) acquires polyhedron information (first information). Then, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding a crystal structure that the composition of the material as a three-dimensional structure can have. In this case, the generation unit 12 generates the second information based not only on the material information and the arrangement information, but also on the polyhedron information.

[0208] On the other hand, even if the user selects the second execution icon in the first image shown in Fig. 35, the generator 12 (in the step of generating second information) generates second information regarding a crystal structure that the composition of the material as a three-dimensional structure can have. In this case, the generator 12 generates the second information based on the material information and the arrangement information.

[0209] 36 shows an example of the second image displayed on the display unit 3. The second image is displayed on the display unit 3 after the generation unit 12 generates second information related to the three-dimensional structure (here, the crystal structure). The second image includes a list of the crystal structures generated by the generation unit 12 and an execution icon labeled "Export selected crystal structure."

[0210] The user selects the crystal structure to be saved and selects the execution icon. Then, the user selects a desired saving format, as in the first embodiment, and the second information regarding the crystal structure selected by the user is saved in the second storage unit 5.

[0211] A second operation example of the entire information processing system 200 according to embodiment 2 will be described below with reference to the drawings. Fig. 37 is a sequence diagram showing a second operation example of the information processing system 200 according to embodiment 2, the display unit 3, the first storage unit 4, and the second storage unit 5. Here, the description will be given assuming that the user inputs polyhedron information.

[0212] (Step S701) The acquisition unit 11 of the information processing system 200 acquires material information and placement information. Here, the material information is acquired by the acquisition unit 11 when the user inputs (selects) the material information using the input unit 2 while viewing the first image (see FIG. 31 ) that is displayed first on the display unit 3. Also, the placement information is acquired by the acquisition unit 11 when the user inputs (selects) the material information using the input unit 2 while viewing the first image (see FIG. 32 ) that is displayed second on the display unit 3.

[0213] (Step S702) The acquisition unit 11 of the information processing system 200 acquires first information. Here, the first information is polyhedron information, and is acquired by the acquisition unit 11 when the user inputs (selects) the first information using the input unit 2 while viewing the first image displayed on the display unit 3.

[0214] (Step S703) The generation unit 12 of the information processing system 200 executes a process of converting the polyhedron code determined to be convertible into a three-dimensional structure. Note that step S703 is the same process as step S505 (see FIG. 27). Furthermore, between step S702 and step S703, the same processes as steps S502 to S504 (see FIG. 27) are executed.

[0215] (Step S704) The generation unit 12 of the information processing system 200 generates multiple arrangement pattern candidates for each generated three-dimensional structure. The arrangement pattern candidates are candidate patterns of elements (atoms) arranged at each vertex and center of each polyhedron included in the three-dimensional structure. Note that the arrangement pattern candidates may also include a pattern in which no element is arranged at the center of a polyhedron.

[0216] (Step S705) The generation unit 12 of the information processing system 200 generates a crystal structure for each arrangement pattern candidate. Specifically, the generation unit 12 generates a crystal structure by arranging elements (atoms) at each vertex and center of each polyhedron according to the arrangement pattern candidate.

[0217] (Step S706) The display unit 3 displays the second image representing the second information on the crystal structure output from the output unit 13 of the information processing system 200.

[0218] (Step S707) When the user selects a crystal structure to be saved while viewing the second image displayed on the display unit 3, the information processing system 200 provides the second information regarding the selected crystal structure to the second storage unit 5. As a result, the second storage unit 5 saves the second information regarding the crystal structure selected by the user.

[0219] As described above, in the second embodiment, by inputting material information related to the composition of a material, it becomes possible to comprehensively generate a three-dimensional structure (i.e., a space-filling structure in a three-dimensional space) that is formed by combining multiple polyhedra based on the input material information. Therefore, in the second embodiment, a three-dimensional structure can be generated for a material that the user wants to search for.

[0220] (Third Embodiment) Hereinafter, an information processing system 300 (information processing method or program) according to a third embodiment of the present disclosure will be described in detail with reference to the drawings. FIG. 38 is a block diagram showing an overall configuration including the information processing system 300 according to the third embodiment. The information processing system 300 according to the third embodiment differs from the information processing system 100 according to the first embodiment in that the acquisition unit 11 further acquires third information related to the use of the three-dimensional structure. The information processing system 300 according to the third embodiment also differs from the information processing system 100 according to the first embodiment in that a third storage unit 6 is further connected. Note that the information processing system 300 according to the third embodiment includes the acquisition unit 11, the generation unit 12, and the output unit 13, similar to the information processing system 100 according to the first embodiment, and since the configuration is the same, description of these components will be omitted.

[0221] The third storage unit 6 is a recording medium for storing a use database relating to uses of the three-dimensional structure. The recording medium is, for example, a hard disk drive, a RAM (Random Access Memory), a ROM (Read Only Memory), or a semiconductor memory. Note that such a recording medium may be volatile or non-volatile.

[0222] The application database may include data about applications such as architecture, decoration, interior design, toys, urban design, storage, or food.

[0223] Data about buildings may include, for example, data about strengthening or lightening the framework of a building, designing a building in space or the Metaverse (virtual space), or data about buildings in general, such as monuments. Information about the use of a building may include, for example, data about legal regulations such as building codes, data about the properties of building materials, data about land or space, data about residents, data about rules in the Metaverse, or data about budgets.

[0224] Data about an ornament may include data about the appearance of the ornament, such as a pendant, earrings, or ring, etc. Information about the use of the ornament may include data about the physical properties of the material of the ornament, data about its size, etc.

[0225] The data about the interior use may include data about the interior aspects, such as shelving, lighting fixtures, or monuments. The information about the interior use may also include data about the physical properties of the interior materials, data about the size, or data about weight limits, etc.

[0226] The data about the toy may include data about the toy's features, such as building blocks or puzzles, etc. The information about the toy's use may include data about the physical properties of the toy's material, the target age group, the size of the user's hand, or the difficulty level of the toy.

[0227] Data about urban design may include data about road designs, such as roads in the sky, roads in space, or roads in the Metaverse. Data about urban design uses may include data about divisions, such as spatial boundaries. Data about urban design uses may include data about layouts, such as drone placements or store placements in the Metaverse. Data about urban design uses may include data about residents, topography, climate, or culture, data about infrastructure (such as water, sewer, electricity, or gas), data about areas (commercial areas, residential areas, or industrial areas), data about budgets, data about drones, data about stores, data about laws and regulations, etc.

[0228] The storage data may include, for example, data on the manner in which a storage container can be filled to 100%. The storage use data may include, for example, data on the physical properties of the container or contents, data on the size of the container, or data on the contents (fragile, upside down, etc.).

[0229] Data about food may include data about the type of dish, such as a cake, etc. Data about the use of food may include data about the physical properties of the ingredients in the dish, data about the size, etc.

[0230] [Usage Example] Hereinafter, a description will be given of a usage example of the information processing system 300 according to embodiment 3. Fig. 39 is a diagram showing an image displayed on the display unit 3 in usage example 1 of embodiment 3. Fig. 39 shows an example of a first image and a third image displayed on the display unit 3.

[0231] The first image includes a shape selection area, a number specification area, a unit feature selection area, and an execution icon for "Generate 3D structure." The first image is only required to include the shape selection area; the number specification area and the unit feature selection area are not essential. The first image may also include at least one of the number specification area, the unit feature selection area, the symmetry specification area, the composition ratio specification area, and the skewness specification area.

[0232] The third image includes a use selection area for selecting a use of the three-dimensional structure. The use selection area displays names of a plurality of uses selectable by the user and a plurality of selection buttons corresponding to the plurality of uses. Note that the use selection area may display an image of each use along with the name of each use.

[0233] The user selects the purpose of the three-dimensional structure in the purpose selection area. As a result, the acquisition unit 11 (in the step of acquiring third information) acquires third information regarding the purpose of the three-dimensional structure. In this case, when the user selects the execution icon, the generation unit 12 (in the step of generating second information) generates second information regarding the three-dimensional structure to which information based on the purpose indicated by the third information has been added.

[0234] 39, the user selects "material" as the use of the three-dimensional structure. Therefore, in this case, the generation unit 12 generates the second information on the three-dimensional structure of the material, that is, the crystal structure.

[0235] Here, the third image may further include a detailed input image for inputting detailed information about the use of the three-dimensional structure. For example, the detailed input image is displayed on the display unit 3 when the user selects the use of the three-dimensional structure in the use selection area. The detailed input image includes an area for inputting detailed information about the use selected by the user. The detailed input image is displayed on the display unit 3 by the output unit 13 by reading out data corresponding to the use specified by the user, which is stored in the third storage unit 6.

[0236] When the user inputs detailed information in the detailed input image, the acquisition unit 11 (in the step of generating third information) acquires further detailed information about the use of the three-dimensional structure. In this case, the generation unit 12 (in the step of generating second information) generates second information about the three-dimensional structure to which the further detailed information is added as information based on the use indicated by the third information.

[0237] For example, if the user selects "material" as the use of the three-dimensional structure, the detailed input image includes the element selection area or composition designation area and the arrangement designation area in embodiment 2. In this case, the user can specify the types of elements (atoms) included in the three-dimensional structure (i.e., crystal structure) of the material generated by the generation unit 12 and the arrangement of the elements by inputting information into each of the element selection area or composition designation area and the arrangement designation area.

[0238] 39 , the first image and the third image are simultaneously displayed on the display unit 3, but this is not limiting. For example, the third image may be displayed separately from the first image. Specifically, the third image may be displayed before the first image is displayed on the display unit 3, or after the first image is displayed on the display unit 3.

[0239] Below are listed examples of the three-dimensional structures for each purpose generated by the generation unit 12. The examples shown below are examples of three-dimensional structures generated by the generation unit 12 when the user selects the purpose of the three-dimensional structure in the purpose selection area and inputs detailed information about the specified purpose in the detailed input image.

[0240] Fig. 40 is a diagram showing an example of a three-dimensional structure related to a building. The three-dimensional structure shown in Fig. 40 shows a residential facility such as an apartment building in outer space or the Metaverse. In the example shown in Fig. 40, each polyhedron represents a living space.

[0241] Fig. 41 is a diagram showing an example of a three-dimensional structure of an ornament. The three-dimensional structure shown in Fig. 41 shows the structure of a pendant.

[0242] Fig. 42 is a diagram showing an example of a three-dimensional structure related to an interior. The three-dimensional structure shown in Fig. 42 shows the structure of the fixture body of a lighting fixture.

[0243] Fig. 43 is a diagram showing an example of a three-dimensional structure related to a toy. The three-dimensional structure shown in Fig. 43 shows the structure of an assembly block. The image on the far left in Fig. 43 shows an example of a completed image of the assembly block, and the three images on the right in Fig. 43 show examples of blocks included in the assembly block.

[0244] FIG. 44 is a diagram showing an example of a three-dimensional structure related to urban design. The three-dimensional structure shown in (a) of FIG. 44 shows the route of a spaceship in outer space. In (a) of FIG. 44, the edges of each polyhedron represent the route of the spaceship, and the center of each polyhedron represents a planet or the like from which the spaceship takes off or lands. The three-dimensional structure shown in (b) of FIG. 44 shows the movement path of a drone. In (b) of FIG. 44, the edges of each polyhedron represent the movement path of the drone, and the vertices of each polyhedron represent the takeoff and landing points of the drone.

[0245] Fig. 45 is a diagram showing an example of a three-dimensional structure related to storage. The three-dimensional structure shown in Fig. 45 shows a structure that can be stored in a cubic cardboard box (container) with a filling rate of 100%. In Fig. 45, each polyhedron represents an item to be stored in the cardboard box.

[0246] Fig. 46 is a diagram showing an example of a three-dimensional structure related to food. The three-dimensional structure shown in Fig. 46 represents the structure of a cake, in other words, the design of the cake.

[0247] FIG. 47 is a diagram showing an example of a three-dimensional structure related to a material. The three-dimensional structure shown in FIG. 47 is a crystalline structure. In the example shown in FIG. 47, the three-dimensional structure is displayed in a virtual space that can be viewed by the user through a virtual reality (VR) head-mounted display worn by the user. Therefore, the user can edit the crystalline structure using a VR controller while viewing the crystalline structure in the virtual space.

[0248] As described above, in the third embodiment, by inputting the third information relating to the use of the three-dimensional structure, it is possible to comprehensively generate three-dimensional structures (i.e., space-filling structures in three-dimensional space) according to the input use. Therefore, in the third embodiment, it is possible to generate three-dimensional structures according to the use desired by the user.

[0249] (Modifications) The information processing system (information processing method) according to one or more aspects of the present disclosure has been described above based on each embodiment, but the present disclosure is not limited to those embodiments. Various modifications conceivable by a person skilled in the art to the above embodiments may also be included in the present disclosure, as long as they do not deviate from the spirit of the present disclosure. Furthermore, the present disclosure may also include a configuration constructed by combining components of multiple different embodiments.

[0250] For example, in each of the above embodiments, the second information is information indicating the three-dimensional structure itself, but is not limited to this. For example, the second information may include at least one of information indicating the three-dimensional structure, information indicating a sequence representing the three-dimensional structure (e.g., a polyhedral code), and information indicating a periodic graph representing the three-dimensional structure.

[0251] For example, in each of the above-described embodiments, the information processing systems 100, 200, and 300 display the first image or the second image on the display unit 3, but this is not limiting. For example, the information processing systems 100, 200, and 300 may output information included in the first image or the second image without displaying the first image or the second image itself on the display unit 3. Similarly, the information processing system 300 may output information included in the third image without displaying the third image itself on the display unit 3.

[0252] In addition, in each of the above-described embodiments, the acquisition unit 11 of the information processing systems 100, 200, and 300 acquires the first information input by the user via the input unit 2, but this is not limiting. For example, the acquisition unit 11 may acquire the first information by reading information stored in the first storage unit 4 without receiving an input from the user.

[0253] In addition, in each of the above-described embodiments, the first storage unit 4 and the second storage unit 5 are realized by different recording media, but this is not limited to this. For example, the first storage unit 4 and the second storage unit 5 may be realized by the same recording medium. Similarly, in the third embodiment, the first storage unit 4, the second storage unit 5, and the third storage unit 6 may be realized by the same recording medium.

[0254] Furthermore, in the above-described embodiments, each of the information processing systems 100, 200, and 300 is configured with an acquisition unit 11, a generation unit 12, and an output unit 13, but is not limited to this. For example, the information processing system 100 may include a display control unit 30 and a display unit 3, as shown by "100A" in FIG. 5 . Furthermore, the information processing system 300 may include a display control unit 30 and a display unit 3, as shown by "300A" in FIG. 38 . Similarly, the information processing system 200 may include a display control unit 30 and a display unit 3.

[0255] In each of the above embodiments, each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for that component. Each component may be realized by a program execution unit such as a CPU (Central Processing Unit) or a processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.

[0256] The following cases are also included in this disclosure:

[0257] (1) The at least one device is specifically a computer system comprising a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), a hard disk unit, a display unit, a keyboard, a mouse, etc. A computer program is stored in the RAM or hard disk unit. The at least one device achieves its function when the microprocessor operates in accordance with the computer program. Here, the computer program is composed of a combination of multiple instruction codes that indicate commands to a computer to achieve a predetermined function.

[0258] (2) Some or all of the components constituting at least one of the above devices may be configured as a single system LSI (Large Scale Integration). A system LSI is an ultra-multifunctional LSI manufactured by integrating multiple components on a single chip, and specifically, is a computer system configured to include a microprocessor, ROM, RAM, etc. A computer program is stored in the RAM. The system LSI achieves its functions by the microprocessor operating in accordance with the computer program.

[0259] (3) Some or all of the components constituting at least one of the above devices may be configured as an IC card or a standalone module that can be attached to the device. The IC card or module is a computer system composed of a microprocessor, ROM, RAM, etc. The IC card or module may include the above-mentioned ultra-multifunctional LSI. The IC card or module achieves its functions when the microprocessor operates in accordance with a computer program. This IC card or module may be tamper-resistant.

[0260] (4) The present disclosure may be embodied as the methods described above, a computer program that implements these methods on a computer, or a digital signal that includes the computer program.

[0261] The present disclosure may also be a computer program or a digital signal recorded on a computer-readable recording medium, such as a flexible disk, a hard disk, a CD (Compact Disc)-ROM, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray (registered trademark) Disc), a semiconductor memory, etc. Alternatively, the present disclosure may be a digital signal recorded on such a recording medium.

[0262] The present disclosure may also be applied to transmitting a computer program or digital signal via a telecommunications line, a wireless or wired communication line, a network such as the Internet, data broadcasting, or the like.

[0263] Furthermore, the program or digital signal may be recorded on a recording medium and transferred, or the program or digital signal may be transferred via a network or the like, so that the program or digital signal may be implemented by another independent computer system.

[0264] (Others) Modifications of the embodiment of the present disclosure may be as follows.

[0265] 1. A method being performed by one or more processors configured to execute instructions stored in one or more memories, the method comprising: receiving shape information including first information on the shape of a first polyhedron, .about., and nth information on the shape of an nth polyhedron, wherein n is an integer greater than or equal to 1; receiving number information including a first number, .about., and an nth number corresponding to the nth polyhedron, thereby determining one or more first polyhedrons, .about., the nth polyhedron, and one or more nth polyhedrons corresponding to the nth number; rearranging a plurality of codes including one or more first codes, ..., and one or more nth codes, thereby determining a plurality of polyhedron codes (see, for example, Figure 23), wherein the one or more first codes correspond to the first number and a first code for the first polyhedron, ..., and the one or more nth codes correspond to the n number and an nth code for the nth polyhedron, wherein the first code is determined based on the number of sides of each of a plurality of faces included in the first polyhedron, ..., and the nth code is determined based on the number of sides of each of a plurality of faces included in the nth polyhedron (see, for example, Figures 20, 21, and 22); determining a three-dimensional structure including the one or more first polyhedrons, ..., and the one or more nth polyhedrons based on the plurality of polyhedron codes (see, for example, Figure 24); generating second information including an image of the three-dimensional structure and a plurality of three-dimensional coordinates included in the three-dimensional structure; and outputting the image and the second information. The three-dimensional structure does not include one or more polyhedra other than the one or more first polyhedra, ..., and the one or more nth polyhedra; two polyhedra arbitrarily selected from the one or more first polyhedra, ..., and the one or more nth polyhedra do not overlap; and a plurality of positions included in the three-dimensional structure correspond to a plurality of positions of a plurality of atoms included in a crystal structure.

[0266] The present disclosure is useful when exploring unknown materials.

[0267] REFERENCE SIGNS LIST 11 Acquisition unit 12 Generation unit 13 Output unit 2 Input unit 3 Display unit 30 Display control unit 4 First storage unit 5 Second storage unit 6 Third storage unit 100, 200, 300 Information processing system 100A, 300A Information processing system

Claims

1. A computer-implemented information processing method, comprising: acquiring first information about a plurality of polyhedrons including two or more types of polyhedrons having different shapes; generating second information regarding the three-dimensional structure in which the plurality of polyhedrons are arranged without gaps when it is determined based on the first information that a three-dimensional structure in which the plurality of polyhedrons are arranged without gaps is established; and outputting the generated second information. Information processing methods.

2. the second information includes at least one of information indicating the three-dimensional structure, information indicating a sequence including numbers or letters representing the three-dimensional structure, and information indicating a periodic graph representing the three-dimensional structure; The information processing method according to claim 1 .

3. In the step of acquiring the first information, shape information indicating a shape of each of the plurality of polyhedrons is acquired as the first information; In the step of generating the second information, the second information is generated regarding the three-dimensional structure in which the plurality of polyhedrons having the shape indicated by the shape information are arranged without any gaps.

3. The information processing method according to claim 1 or 2.

4. In the step of acquiring the first information, number information indicating the number of each shape of the plurality of polyhedrons is further acquired as the first information, In the step of generating the second information, the second information is generated regarding the three-dimensional structure in which the plurality of polyhedrons having the shapes indicated by the shape information are arranged without gaps in the number for each shape indicated by the number information. The information processing method according to claim 3 .

5. In the step of acquiring the first information, the first information includes shapes of the plurality of polyhedrons. Further obtain composition ratio information showing the composition ratio of each In the step of generating the second information, the second information is generated regarding the three-dimensional structure in which the plurality of polyhedrons having the shapes indicated by the shape information are arranged without gaps at the composition ratios for each shape indicated by the composition ratio information. The information processing method according to claim 3 .

6. An information processing method executed by a computer, comprising: acquiring first information about a plurality of polyhedrons including two or more types of polyhedrons having different shapes; generating second information about a three-dimensional structure in which the plurality of polyhedrons are arranged based on the first information; and outputting the generated second information, the three-dimensional structure is a structure in which the plurality of polyhedrons are arranged without any gaps, In the step of acquiring the first information, skewness information indicating an allowable skewness of the shapes of the plurality of polyhedrons is acquired as the first information; In the step of generating the second information, the second information is generated regarding the three-dimensional structure in which at least a part of the plurality of polyhedrons is distorted so that the distortion does not exceed the distortion indicated by the distortion information. Information processing methods.

7. In the step of acquiring the first information, shape information indicating the shape of each of the plurality of polyhedrons is further acquired as the first information; the skewness is determined based on at least one of the position of the center of gravity of the polyhedron, the position of at least one vertex of the polyhedron, the length of at least one side of the polyhedron, the angle formed by at least two sides of the polyhedron, and the area of ​​at least one face of the polyhedron, with the shape of the polyhedron indicated by the shape information as a reference. The information processing method according to claim 6.

8. obtaining third information relating to a use of the three-dimensional structure; In the step of generating the second information, the second information about the three-dimensional structure is generated by adding information based on the purpose indicated by the third information to the three-dimensional structure generated based on the first information.

3. The information processing method according to claim 1 or 2.

9. The step of generating second information includes: converting the acquired first information into a plurality of first number sequences that respectively represent the plurality of polyhedra; and converting a second number sequence representing a polytope generated using the converted plurality of first number sequences into the three-dimensional structure.

3. The information processing method according to claim 1 or 2.

10. The step of generating second information includes: converting the acquired first information into a plurality of polyhedron graphs respectively representing the plurality of polyhedra; and converting a cyclic graph generated using the converted polyhedral graphs into the three-dimensional structure.

3. The information processing method according to claim 1 or 2.

11. a display control unit that displays on the display unit a first image that accepts input of first information about a plurality of polyhedrons including two or more types of polyhedrons that are different in shape from each other, and then displays on the display unit a second image that represents second information about the three-dimensional structure in which the plurality of polyhedrons are arranged without gaps, the second information being generated when it is determined that a three-dimensional structure in which the plurality of polyhedrons are arranged without gaps is established based on the input first information. Information processing system.

12. the display control unit further displays a third image on the display unit that accepts input of third information related to an application of the three-dimensional structure; the three-dimensional structure is generated based on the input first information and is a structure to which information based on the purpose indicated by the input third information is added; The information processing system according to claim 11.

13. acquiring first information about a plurality of polyhedrons including two or more types of polyhedrons having different shapes; generating second information regarding the three-dimensional structure in which the plurality of polyhedrons are arranged without gaps when it is determined based on the first information that a three-dimensional structure in which the plurality of polyhedrons are arranged without gaps is established; and outputting the generated second information. program.