Three-dimensional assembly having identical pentahedrons

Abstract

A modular three-dimensional assembly comprising a plurality of identical pentahedrons, each with five vertices, eight edges of varying lengths, and five faces— specifically, one right-angled trapezium, three right triangles, and one isosceles obtuse triangle. Each pentahedron face includes at least one coupling mechanism, configured to detachably connect with corresponding mechanisms on adjacent units, utilizing a combination of protrusions and recesses.

Description

DescriptionTitle of Invention: Three-Dimensional Assembly havingIdentical Pentahedrons

[0001] This application claims priority from International Patent Application No.PCT / IB2023 / 061888, filed on 25 / 11 / 2023, under the Patent Cooperation Treaty(PCT). The entirety of the disclosure of the earlier application is incorporated herein by reference.Technical Field

[0002] The present invention generally relates to assemblies, particularly modular three-dimensional structures composed of polyhedral units. More specifically, the invention pertains to the design and construction of three-dimensional assemblies using identical pentahedrons, which can be used in various applications including educational tools, architectural design, modular construction systems, modular containers, and recreational or decorative purposes. The invention is particularly relevant to the areas of mathematical modeling, geometric design, and modular architecture, where the ability to easily assemble and reconfigure various shapes is of significant utility.Background Art

[0003] In assemblies, polyhedral shapes such as cubes, tetrahedrons, and dodecahedrons have been widely used for constructing modular systems, geometric puzzles, and educational models. These shapes are often employed due to their simplicity and ease of assembly, which facilitate the construction of basic three-dimensional structures. However, while these traditional polyhedral forms effectively create simple structures, they often fall short when more intricate designs are required, necessitating additional components or different geometric shapes.

[0004] Modular construction systems that utilize polyhedral units have been developed for various applications, including architectural designs and educational tools. These systems typically involve connecting individual geometric shapes to form larger structures. However, existing systems are often constrained by the regularity and uniformity of the shapes used, which restricts the range of possible configurations, resulting in less dynamic and flexible designs. More versatiledesigns, while available, generally require multiple parts and different shapes, adding to the complexity and cost of the system.

[0005] Additionally, the coupling mechanisms used in current polyhedral assemblies, though functional, may not provide the level of flexibility or stability required for more complex assemblies. This can hinder stable connections and reconfiguration, a critical consideration in modular construction systems.

[0006] Moreover, conventional pentahedrons, when used to form a cube, pose a manufacturing challenge due to the need for identical coupling mechanisms on each face. Since each face of the pentahedron may connect to multiple other faces, the coupling mechanisms on each face must be identical to ensure seamless connectivity. If the coupling mechanisms are not identical, multiple molding configurations would be required, adding complexity and cost to the manufacturing process.

[0007] These limitations highlight the need for an improved geometric assembly that enables more versatile and flexible designs, and also overcomes the manufacturing challenges of producing complex shapes as single pieces using standard molding techniques or other methods.Summary of Invention

[0008] This summary is a brief overview of the invention and is not a comprehensive or definitive description. It is not intended to identify essential features, nor is it intended to limit the scope of the invention. The proper scope of the present disclosure may be ascertained from the claims set forth below, given the detailed description and the drawings below.

[0009] Certain embodiments of the present invention may provide a modular three- dimensional assembly. In one general aspect, the modular three-dimensional assembly may include a plurality of identical pentahedrons. Each pentahedron may be designed with five vertices, eight edges of varying lengths, and five faces. The faces may comprise one right-angled trapezium face, three right triangle faces, and one isosceles obtuse triangle face.

[0010] In any aspect, each of the identical pentahedrons may comprise five distinct edge lengths, such that three edges with a length of one unit, two edges with a length of the square root of one and one-quarter ( l .25) units, one edge with alength of the square root of three ( 3) units, one edge with a length of the square root of two (> / 2) units, and one edge with a length of one-half of the unit.

[0011] In one aspect, each face of the identical pentahedrons may be equipped with at least one coupling mechanism. In one preferred aspect, the coupling mechanisms may include a combination of protrusions and recesses, and may be configured to detachably connect with corresponding coupling mechanisms on adjacent pentahedrons.

[0012] In one particular aspect, the right triangle face may include two coupling mechanisms, each of which is designed to connect with identical mechanisms on adjacent pentahedrons. Additionally, coupling mechanisms on other faces, such as the right-angled trapezium face and isosceles obtuse triangle face, are designed to engage with corresponding identical mechanisms on adjacent pentahedrons.Technical Problem

[0013] The present invention addresses several challenges encountered in the design and construction of modular three-dimensional assemblies using polyhedral units. Existing systems that utilize polyhedral shapes, such as cubes, tetrahedrons, and dodecahedrons, often suffer from limitations related to flexibility, versatility, and ease of assembly. Traditional modular systems are constrained by the uniformity of the shapes used, which restricts the range of possible configurations, resulting in less dynamic and flexible designs. Furthermore, conventional polyhedral shapes require multiple parts or different geometric forms, which increases complexity and manufacturing costs. The coupling mechanisms used in existing systems also fail to provide the level of stability and flexibility needed for assembling complex structures. Additionally, manufacturing challenges arise when identical coupling mechanisms must be incorporated on each face of polyhedral units. These limitations highlight the need for a modular assembly system that can offer greater design versatility, manufacturing efficiency, and reconfigurability.Solution to Problem

[0014] The present invention provides a novel solution to the limitations of traditional modular polyhedral assemblies by introducing a system based on modular three- dimensional assemblies composed of identical pentahedrons. These pentahedrons are specifically designed with a combination of distinct geometricshapes and coupling mechanisms that enable flexible, stable, and reconfigurable assembly. Each pentahedron has five faces, including a right-angled trapezium face, right triangle faces, and an isosceles obtuse triangle face, all of which are equipped with protrusions and recesses designed to interconnect with corresponding coupling mechanisms on adjacent pentahedrons. This modular design allows for the easy assembly of complex structures, such as cubes, rectangular prisms, and irregular polyhedra, without the need for multiple distinct parts or different geometric shapes.

[0015] The coupling mechanisms are configured to ensure stable, detachable connections between the pentahedrons, which enhances the flexibility and stability of the assembled structure. Additionally, the identical nature of the pentahedrons simplifies the manufacturing process by eliminating the need for different parts or specialized molding techniques for each unit. The use of a single, uniform coupling mechanism on each face allows for mass production using standard molding techniques, reducing both complexity and production costs.

[0016] This solution provides a versatile and scalable system that can be used in various applications, such as educational tools, architectural design, modular construction, and recreational purposes. It also eliminates the production difficulties associated with creating multiple distinct polyhedral shapes, enabling cost-effective and efficient manufacturing.Brief Description of Drawings

[0017] The present invention is best understood by referencing the following description and accompanying figures. These figures are given purely by way of indication and in no way restrict the scope of the application. Of these figures:

[0018] FIG. 1 illustrates individual face views and a top view of the pentahedron in accordance with one or more exemplary embodiments of the present disclosure.

[0019] FIG. 2A illustrates a perspective view of the pentahedron shown in FIG. 1, including coupling mechanisms on two faces in accordance with one or more exemplary embodiments of the present disclosure.

[0020] FIG. 2B is another perspective view of the pentahedron shown in FIG. 1 , including coupling mechanisms on two faces in accordance with one or more exemplary embodiments of the present disclosure.

[0021] FIG. 2C is yet another perspective view of the pentahedron shown in FIG. 1 , including coupling mechanisms on three faces in accordance with one or more exemplary embodiments of the present disclosure.

[0022] FIG. 3 illustrates various stages of assembling identical pentahedrons into a cube spatial assembly, in accordance with one or more exemplary embodiments of the present disclosure.

[0023] FIGS. 4A and 4B illustrate one exemplary embodiment of the invention, showing the assembly used as modular containers in a particular application in accordance with one or more exemplary embodiments of the present disclosure.Description of Embodiments

[0024] In the following detailed description, reference is made to the accompanying drawings, which form a part hereof and are shown by way of illustration of example embodiments or aspects in which the disclosure may be practiced. The drawings are not drawn to scale and are intended to illustrate the principles of the disclosure rather than to show actual dimensions or proportions. However, it will be evident to one skilled in the art that an example embodiment may be practiced without all of the disclosed details.

[0025] The present disclosure is not intended to be limited to the specific embodiments described herein, and it is contemplated that various changes, substitutions, and equivalents may be made without departing from the scope of the disclosure. The detailed description that follows is provided by way of illustration, and is not intended to be limiting. Additionally, throughout this specification, the terms "a", "an", and "the" are intended to include plural references, and the term "in" is intended to include both "in" and "on".

[0026] It is to be understood that the use of phrases such as 'an embodiment,' 'one embodiment,' or 'an example embodiment' in this specification is intended to provide illustrative examples, and not to imply that the corresponding embodiment is limited to the specific features, structures, or characteristics described.

[0027] As used herein, the terms "assembly" and "three-dimensional assembly" are used interchangeably to refer to a modular structure composed of multiple identical pentahedrons. The terms 'identical pentahedrons' and 'pentahedrons' are used interchangeably to describe these polyhedral, each having eight edges and fivevertices, and including at least one coupling mechanism on each face. These pentahedrons are interconnected through coupling mechanisms to form the modular three-dimensional assembly.

[0028] The present disclosure relates to various embodiments and aspects of a modular three-dimensional assembly comprising a plurality of identical pentahedrons. This assembly may be characterized by its flexibility, reconfigurability, and modular nature, allowing it to adapt to diverse applications such as modular construction, geometric modeling, educational tools, and architectural designs. The modular assembly may include interconnected pentahedrons designed to form larger and more complex three-dimensional structures, including but not limited to cubes, rectangular prisms, and irregular polyhedra. Each pentahedron may be identical in structure and designed with five vertices, eight edges, and five distinct faces. Together, the plurality of interconnected pentahedrons in this modular design allows for the assembly of flexible and reconfigurable structures, which can be adapted for various applications.

[0029] FIG. 1 and FIGS. 2A-2C collectively illustrate one exemplary embodiment of a pentahedron 100 from various perspectives. FIG. 1 shows individual face views and a top view of the pentahedron 100, while FIGS. 2A-2C present perspective views of the pentahedron 100 from different angles. These figures may provide a detailed visualization of the pentahedron’s geometric structure, which is fundamental to the modular assembly’s reconfigurability. Together, these figures may demonstrate the geometric configuration of the pentahedron 100 and layout of its coupling mechanisms.

[0030] The assembly design may vary according to specific needs. In one exemplary embodiment, as depicted in FIG. 1, the pentahedron 100 may comprise five faces: one face configured as a right-angled trapezium 101, three faces configured as right triangles 105, 107, 109, and one face configured as an isosceles obtuse triangle 103. These features can enable each pentahedron to interact seamlessly with other identical units, contributing to the assembly’s modularity and structural versatility. Each of these faces may contribute to the unique geometry of the pentahedron 100, allowing for versatile structural configurations when multiple pentahedrons are assembled.

[0031] In this exemplary embodiment, each face of the pentahedron 100 may include coupling mechanisms comprising a combination of protrusions and recesses. These coupling mechanisms may be designed to enable detachable and stable connections between adjacent pentahedrons, thereby forming the modular assembly. As shown in FIG. 2A, the right triangle face 109 may incorporate two protrusions designed to engage with corresponding recesses on the right-angled trapezium face 101 of an adjacent pentahedron. Similarly, the coupling mechanisms on the isosceles obtuse triangle face 103, as well as on the right triangle faces 105 and 107, may be designed to securely engage with identical coupling mechanism on adjacent pentahedrons. The arrangement of these coupling mechanisms can ensure precise alignment and interconnectivity of pentahedrons, forming stable and reconfigurable assemblies.

[0032] The combination of protrusions and recesses in this exemplary embodiment, may be designed to provide stable and detachable connections between adjacent pentahedrons 100. The interlocking functionality and design of the protrusions and recesses can restrict relative movement between adjacent pentahedrons, thereby enhancing the stability of the assembled structure as multiple connections are made. This design can also enable the assembled structure to be readily reconfigured or disassembled, thereby broadening its adaptability for different applications such as modular construction, educational models, and toys.

[0033] In some embodiments, the coupling mechanism may include additional features such as magnetic elements. These magnetic elements, which in some exemplary embodiments, may be permanent, can be embedded within the faces to enable detachable magnetic connections between adjacent pentahedrons. Various methods, such as adhesives or mechanical fasteners, may be used to secure the magnetic elements to the faces, offering flexible options for the assembly configuration.

[0034] In one embodiment, the modular assemblies and its pentahedrons 100 may be produced using molding techniques, such as straight-pull injection molding process, to ensure efficient production of identical pentahedrons while minimizing complexity and cost. This design may eliminate negative draft angles, which could complicate part ejection, thereby allowing for a smooth release from the mold. The mold cavity may be formed by two cooperating mold halves that close along aparting line positioned perpendicular to the mold closure direction. For instance, this parting line may be positioned along edges 121 and 111 , and extend across the longest diagonal of the right-angled trapezium face 131. By minimizing negative draft angles, this design may reduce production complexity and costs, facilitating large-scale manufacturing of consistent and precise pentahedron units.

[0035] In one preferred embodiment, the pentahedron 100 may be configured with specific edge lengths that contribute to its geometric structure and functional versatility. These edge lengths may be essential for ensuring the precision and modularity of the assembly, facilitating seamless alignment and connectivity between adjacent pentahedrons. As illustrated in FIGS. 2A-2C, the pentahedron 100 may include eight edges, each assigned a particular length. In this embodiment, three edges 113, 119, 121 may each have a length of one unit. Two edges 115, 123 may each have a length of the square root of one and one-quarter (A / 1.25) units. One edge 111 may have a length of the square root of three ( 3) units, another edge 125 a length of the square root of two ( 2) units, and one edge 117 a length of one-half of a unit. This precise variation in edge lengths may facilitate precise alignment of each face with corresponding faces on adjacent pentahedrons, enabling various configurations when multiple units are assembled.

[0036] Additionally, the edge unit value may be adaptable to suit specific application requirements. As a result, each pentahedron 100 can be produced in a range of sizes, spanning from approximately one centimeter to scales in the order of meters. This scalability can enhance the versatility of the pentahedron-based assembly, making it suitable for diverse applications across various industries, from compact models to substantial structural frameworks.

[0037] As illustrated in FIGS. 2A and 2B, the assembly’s pentahedrons 100 may, in one preferred embodiment, feature a first and a second coupling mechanism on face 105. These coupling mechanisms, designated as 105a and 105b, may each include their own combination of protrusions and recesses, allowing face 105 to engage securely with two adjacent pentahedrons. This design may enhance the modular assembly's stability and interconnectivity, ensuring that the assembly can support dynamic configurations. It should be noted that the terms “first coupling mechanism” and “second coupling mechanism” are used solely for clarity and are not intended to limit the scope of the invention.

[0038] In FIG. 2C, one exemplary embodiment of the pentahedron 100 is depicted from a distinct perspective, revealing three of its faces. This view highlights the spatial orientation of the pentahedron 100, specifically the geometric relationship between the right-angled trapezium face 101 and the adjacent right triangle faces 107 and 109 converging at the right vertex. This configuration illustrates how these faces align to form precise right angles, facilitating accurate connections within the modular assembly and enabling the construction of stable, complex structures.

[0039] FIG. 3 illustrates the assembly of four identical pentahedrons 100 configured to form a cube 303 according to one exemplary embodiment of the present disclosure. This embodiment demonstrates the modular assembly's capability to create stable and symmetrical structures through precise alignment and interconnectivity of identical units. The rotational symmetry axes essential for this configuration are illustrated in FIGS. 2A and 2B. Among this, the symmetry axis 137, representing the second-order rotational symmetry of the cube 303, may facilitate the rotation of the pentahedron 100 to connect with an adjacent pentahedron via the coupling mechanism on face 103. This arrangement thereby can enable the formation of intermediate structure, such as right-angled triangular prism 301 with two adjacent pentahedrons 100.

[0040] In this embodiment, the symmetry axis 133, representing a fourth-order rotational symmetry axis of the cube 303, may allow for rotation and alignment of either the pentahedron 100 or the right-angled triangular prism 301 to connect seamlessly with adjacent pentahedrons via coupling mechanisms 105a and 105b on face 105. This arrangement can form the cube 303 by connecting four pentahedrons 100. Additionally, the outer faces of the cube 303, specifically faces 109 and 101 , may provide connection points for further assemblies facilitating the construction of more complex structures.

[0041] In another embodiment, the right-angled triangular prism 301 may serve as a key element in forming a rectangular cuboid. This configuration may be achieved by connecting four adjacent triangular prisms 301 via the coupling mechanisms on faces 109 and 101. By assembling eight identical pentahedrons 100 in this manner, the arrangement may form the rectangular cuboid, showcasing modular design flexibility.

[0042] In various embodiments, the modular assembly may allow for more configurations beyond the rectangular cuboid and cube 303 may be achieved using assemblies of pentahedrons 100. The pentahedrons 100 can be assembled in multiple orientations, allowing the creation of complex and irregular shapes, as well as modular structures beyond traditional cuboid formations.

[0043] In some embodiments, the pentahedron 100 may feature variations in the design of the combination of protrusions and recesses tailored to its intended use. In one exemplary embodiment, the vertices of the pentahedron 100 and the edges of its coupling mechanisms can incorporate sharper angles, enhancing suitability for precision-demanding applications like construction sets.

[0044] In another embodiment, the assembly may include multiple pentahedrons 100 in varying colors or sizes. The availability of different colors and sizes may enhance the assembly's adaptability of the modular assembly, making it suitable for a wider range of applications, such as educational tools or decorative modular systems.

[0045] The pentahedron 100 of the assembly may be designed to be either solid or hollow, depending on the desired application and implementation. In one embodiment, a solid pentahedron 100 may be particularly useful in applications such as toy construction sets, where solidity could provide structural strength and durability. In an alternative embodiment, a hollow pentahedron 100 may be configured for applications such as modular containers or assembled floating bridges, where a lightweight structure may be advantageous.

[0046] The materials used to produce the pentahedrons 100 of the assembly may vary based on the intended application, structural requirements, and production methods. In one embodiment, the pentahedron 100 may be made from plastics, such as thermoplastics, such as polypropylene, polyethylene, and acrylonitrile butadiene styrene. In another embodiment, thermosetting plastics, such as epoxy or polyester resins, may be used for applications requiring greater rigidity and environmental resistance.

[0047] In addition to traditional manufacturing methods such as injection molding, three-dimensional (3D) printing (additive manufacturing) may also be employed to produce the pentahedrons 100. Materials commonly used in fused depositionmodeling (FDM), such as polylactic acid and ABS, or selective laser sintering with nylon or powdered metals, can be utilized in 3D printing processes.ExamplesExample 1 : Modular Container

[0048] In this example, a particular application of the assembly as modular containers 400 is described, as shown in FIGS. 4A and 4B. According to these exemplary embodiments, the pentahedron 100 may be configured as a modular container 400 designed to securely store liquid substances while maintaining structural integrity.

[0049] FIG. 4A provides an expanded view of the modular container 400 emphasizing its functional components. The modular container 400 may include an opening located adjacent to the interconnecting vertex of four edges — 111 , 121 , 123, and 125 — dividing the modular container 400 into two sections: a body 401 and a cap 403. This configuration may allow for easy filling and sealing of the container, ensuring its practicality in liquid storage.

[0050] As illustrated in FIG. 4B, the modular containers 400 can be interconnected to form larger and cohesive assemblies. In this implementation, the protrusions on faces 103, 105, and 107 of each modular container 400 may be designed to securely engage with the corresponding recesses on identical faces of adjacent modular containers, thereby limiting their relative movement. Additionally, the protrusions on face 109 may engage with the corresponding recesses on face 101. This design may ensure stable connectivity between containers, enabling modular scalability.

[0051] In this example, the assembled modular containers may facilitate efficient liquid storage by arranging modular containers 500 adjacently to form a compact, spacesaving cubic assemblies. This arrangement can enhance storage efficiency and may allow for practical, modular configurations suited for diverse applications.Example 2: Injection Molding Process

[0052] In this example, a specific application of the invention is described, illustrating an injection molding process for producing the pentahedron 100. This manufacturing approach highlights the feasibility of producing complex geometric shapes as single units while maintaining precision and cost-efficiency. In this process, the pentahedron 100 may be molded as a single piece using a straight-pull injection molding technique. This method may involve designing the pentahedron 100 with non-negative draft angles on each face, which can help prevent undercuts and facilitate easy removal of the part from the mold.

[0053] The mold design, as detailed, may include two halves that close along a parting line positioned perpendicular to the mold’s closure direction. In this embodiment, the parting line may be located along two edges — 121 and 111 — and the longest diagonal of the right-angled trapezium face 131. This configuration may allow for efficient molding and separation of the pentahedron without requiring secondary operations or additional molding steps. This placement can ensure efficient separation of the molded part while minimizing the need for secondary operations.

[0054] This approach may enable the mass production of pentahedrons 100 while maintaining precision in their geometric configuration and coupling mechanisms. By eliminating negative draft angles, the molding process may reduce the risk of manufacturing defects and enhances consistency across parts. The absence of negative draft angles may further reduce the likelihood of defects, ensuring consistency and quality across molded parts. This process can be particularly advantageous for applications requiring high production volumes and cost efficiency, such as in the creation of modular toy construction sets or modular containers. The ability to mass-produce these components without compromising quality can further underscore the practicality of this technique.Industrial Applicability

[0055] According to the aforementioned various embodiments, the present invention may be applied to a range of industries requiring modular and reconfigurable assembly systems. In educational and modeling applications, the invention may enable the construction of geometric structures for learning and research. In the fields of construction and architecture, the modular pentahedron assembly may provide stable, interlocking components that can be configured into various structural forms.

[0056] The invention may also be suitable for recreational products, particularly in the creation of toy construction sets, due to its versatility and engaging assembly capabilities. Additionally, the hollow configuration of the pentahedrons may allow for use in storage and container systems, as well as lightweight floating structuresfor transport and assembly in various environments. The adaptability of the pentahedrons in size, material, and color may make this invention suitable for scalable applications in diverse industrial sectors, i

Claims

Claims

1. A modular three-dimensional assembly comprising:- a plurality of identical pentahedrons, wherein each of the plurality of identical pentahedrons, comprising: i. five vertices; ii. eight edges, each having a distinct length; and iii. five faces, wherein:- one face is a right-angled trapezium (101 ),- three faces are right triangles (105, 107, 109), and- one face is an isosceles obtuse triangle (103); wherein each of the plurality of identical pentahedrons comprises five different edge lengths; and wherein each face of the plurality of identical pentahedrons comprises at least one coupling mechanism configured to detachably connect with a corresponding coupling mechanism of at least one adjacent pentahedron.

2. The modular three-dimensional assembly according to claim 1 , wherein each of the plurality of identical pentahedrons further comprises: a. three edges having a length of one unit (113, 119, 121 ); b. two edges having a length of the square root of one and one-quarter units (115, 123); c. one edge having a length of the square root of three units (111 ); d. one edge having a length of the square root of two units (125); e. one edge having a length of one-half of the unit (117).

3. The modular three-dimensional assembly according to claim 1 , wherein the at least one coupling mechanism comprises a combination of protrusions and recesses designed to interlock with corresponding coupling mechanisms on adjacent pentahedrons.

4. The modular three-dimensional assembly according to claim 1 , wherein the coupling mechanism of the right triangle face (105) includes a first and a second coupling mechanism, each configured to detachably connect with an identical corresponding coupling mechanism on the at least one adjacent pentahedron.

5. The modular three-dimensional assembly according to claim 1 , wherein the coupling mechanism of the right triangle face (109) is configured to detachably connect with the coupling mechanism of the right-angled trapezium face (101 ).

6. The modular three-dimensional assembly according to claim 1 , wherein the coupling mechanism of the isosceles obtuse triangle face (103) and the coupling mechanism of the right triangle face (107) are configured to detachably connect with identical corresponding coupling mechanisms on the at least one adjacent pentahedron.

7. The modular three-dimensional assembly according to claim 1 , wherein the identical pentahedrons are configured to assemble into larger structures, including cubes, rectangular prisms, and irregular polyhedra.

8. The modular three-dimensional assembly according to claim 1 , wherein the coupling mechanisms further include magnetic elements to enhance detachable connectivity.

9. The modular three-dimensional assembly according to claim 1 , wherein the identical pentahedrons are manufactured using a straight-pull injection molding technique^

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