Topology structure method for space plane rubik's cube mechanism based on regular hexagonal prism

Abstract

To provide a topology structure method for a space plane Rubik's cube mechanism based on a regular hexagonal prism so as to compose even more Rubik's cube structures in a topology configuration.SOLUTION: Provided is a topology structure method for a space Rubik's cube mechanism on the basis of compatibility by performing analysis according to symmetry between a rotational shaft of a regular hexagonal prism and a turning sub-contact surface and by forming an adjacent matrix.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to the technical field of kinematics, and in particular to a topology construction method for a space planar Rubik's Cube mechanism based on a regular hexagonal prism. [Background technology]

[0002] The Rubik's Cube is a complex mechanism with strong coupling and variable topology, invented by Professor Ernö Rubik of the Hungarian Academy of Architecture in 1974. The Rubik's Cube has attracted widespread attention because of its compact structure and the fact that numerous combinations can be realized by simply rotating it.

[0003] As the recognition and understanding of the Rubik's Cube deepens, researchers have found more and more properties of the Rubik's Cube, such as the property of continuously turning and transforming in space, the property of arranging and recombining, and the property of repeatedly turning. Based on these properties, many products using the Rubik's Cube have been invented, such as the Rubik's Cube satellite, the Rubik's Cube locker, the Rubik's Cube box, the Rubik's Cube microfluidic, and the AIE (Aggregation-Induced Release) Rubik's Cube hydrogel. These applications fully reveal the wide range of applicability and influence of the Rubik's Cube. Generally, a moving system with a certain motion is regarded as a mechanism, so that the moving system can be studied from the perspective of mechanics. The many combination states of the Rubik's Cube are many configuration states or topologies, which intuitively represent the reconfigurable property of the Rubik's Cube mechanism. Moreover, both the conventional Rubik's Cube and its related applications are based on the transformable topology, many states, and reconfigurable properties of the Rubik's Cube. Summary of the Invention [Problem to be solved by the invention]

[0004] In order to widely develop the application of Rubik's Cube and generate more new products for Rubik's Cube, a Rubik's Cube with more configuration types is required, which creates new challenges and needs for the Rubik's Cube mechanism. However, the conventional theories of mechanism and structure, whether the conventional mechanism structure theory that is becoming more and more mature or the reconfigurable mechanism structure theory that is in the early stages of research, are difficult to apply to the structural research of the reconfigurable mechanism of the Rubik's Cube mechanism. Therefore, in order to construct more Rubik's Cube mechanisms that are topology configurations, a topology construction method for the space plane Rubik's Cube mechanism based on a regular hexagonal prism is provided. It is fully necessary for the future research on the Rubik's Cube mechanism and the design of its configuration. [Means for solving the problem]

[0005] In view of the defects existing in the prior art, the present invention provides a topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism based on the characteristics of mechanics. The method includes: setting the rotation axis of the spatial Rubik's Cube mechanism based on the symmetry of the rotation axis of the regular hexagonal prism; setting the turning sub-contact surface of the spatial Rubik's Cube mechanism based on the symmetry of the turning sub-contact surface of the regular hexagonal prism; determining the adjacent matrix of the turning sub-contact surface intersecting based on the intersection of the turning sub-contact surface; constructing a topology construction for the spatial Rubik's Cube mechanism based on the adjacent matrix; setting the rotation axis of the planar Rubik's Cube based on the symmetry of the intersection line of the turning sub-contact surface and the spatial Rubik's Cube mechanism; constructing a topology construction for the planar Rubik's Cube mechanism based on the symmetry of the rotation axis of the planar Rubik's Cube; and constructing a topology construction for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism based on the spatial Rubik's Cube mechanism and the planar Rubik's Cube mechanism. The present invention constructs an adjacency matrix from the symmetry of the rotation axis and the rotating sub-contact surface, and based on compatibility, many more forms are generated for the topological configuration of the spatial Rubik's Cube mechanism.

[0006] The present invention provides a topology construction method for a space planar Rubik's Cube mechanism based on a regular hexagonal prism, the method including the following steps: Step S1: Set the rotation axis of the spatial Rubik's Cube mechanism according to the symmetry of the rotation axis of the regular hexagonal prism. Select the center point of the regular hexagonal prism as the intersection of all the rotation axes, and set the rotation axis of the spatial Rubik's Cube mechanism according to the position of the feature point on the rotation axis. Step S2 sets the turning sub-contact surface of the spatial Rubik's Cube mechanism based on the symmetry of the turning sub-contact surface of the hexagonal prism, divides the rotation axes of the spatial Rubik's Cube mechanism into multiple groups, determines the turning angle required to overlap each group, determines the grouping into the same turning sub-contact surface, and sets the symmetry of the turning sub-contact surface of the spatial Rubik's Cube mechanism. Step S3 is to determine a neighboring area where the turning sub-contact surfaces intersect based on the intersection of the turning sub-contact surfaces. JPEG2024178885000002.jpg7170JPEG2024178885000003.jpg38170JPEG2024178885000004.jpg35170When the sub-contact surfaces do not intersect, the element at the corresponding position in the adjacency matrix becomes 0, among which, when a and b are both constants but are two different constants with values ​​from 1 to n, and a certain column or row in the adjacency matrix are both 0, the corresponding rotation sub-contact surface does not intersect with any of the rotation sub-contact surfaces or is spaced a certain distance apart, and in this state there is no rotation sub-contact surface and no rotation axis. Step S4 constructs a topological configuration for the spatial Rubik's Cube mechanism based on the adjacency matrix. By combining the values ​​of multiple related parameters with 0 or 1 in the adjacency matrix where the turning sub-contact surfaces intersect, a spatial Rubik's Cube mechanism with a different topological configuration is obtained. Step S5: set the rotation axis of the planar Rubik's Cube according to the symmetry between the intersection line of the turning sub-contact surface and the spatial Rubik's Cube mechanism. According to the spatial Rubik's Cube mechanisms with different topological configurations, select the intersection lines of the turning sub-contact surfaces on different faces of the spatial Rubik's Cube mechanism to set the symmetry of the rotation axis of the planar Rubik's Cube. Step S6 constructs a topological configuration for the planar Rubik's Cube mechanism by establishing the symmetry of the rotation axis of the planar Rubik's Cube. Step S7 constructs a topological configuration for the spatial planar Rubik's Cube mechanism of a regular hexagonal prism based on the spatial Rubik's Cube mechanism and the planar Rubik's Cube mechanism. By combining the spatial Rubik's Cube mechanisms of the multiple topological configurations obtained in step S4 and the planar Rubik's Cube mechanisms of the multiple topological configurations obtained in step S6, a spatial planar Rubik's Cube mechanism of a regular hexagonal prism with a different topological configuration is obtained.

[0007] Furthermore, the step S1 specifically includes the following steps. Step S11 obtains a first type of rotation axis configuration for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the centers of the regular hexagonal prism faces respectively. Step S12 obtains a second type of rotation axis configuration for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the vertices of the regular hexagonal prism respectively. Step S13 obtains a third type of rotation axis configuration for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the midpoints of the sides of the regular hexagonal prism respectively. Step S14 obtains a fourth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis partly pass through the center of the regular hexagonal prism face and partly pass through the apex of the regular hexagonal prism. Step S15 obtains a fifth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis partly pass through the vertices of the regular hexagonal prism and partly pass through the midpoints of the sides of the regular hexagonal prism. Step S16 obtains a sixth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis partly pass through the center of the regular hexagonal prism face and partly pass through the midpoint of the side of the regular hexagonal prism.

[0008] Preferably, the step S2 specifically includes the following steps: Step S21: For the six rotation axes passing through the center of the side in the setting of the first type of rotation axes in the spatial Rubik's Cube mechanism obtained in step 11, if the six rotation axes are divided into six groups, step S22 is executed; if the six rotation axes are divided into two groups, step S23 is executed; if the six rotation axes are divided into three groups, step S24 is executed. The turning sub-contact surfaces on the six rotation axes simultaneously intersect with the turning sub-contact surfaces on the rotation axes passing through the centers of both the upper and lower surfaces. Step S22 requires that when there is only one rotation axis in each group, the rotation axes are rotated by an integer multiple of 60° to overlap, and when establishing the symmetry of the rotation sub-contact surfaces, the rotation sub-contact surfaces on the six rotation axes are the same. Step S23, when there are three rotation axes in each group, rotates the rotation axes by an integer multiple of 120° so as to overlap, and when setting the symmetry of the rotation sub-contact surfaces, it is required that the rotation sub-contact surfaces on the three rotation axes in each group are the same, and this is set as the first mode. Step S24, when there are two rotation axes in each group, rotates the rotation axes by an integer multiple of 180° so as to overlap, and when setting the symmetry of the rotation sub-contact surfaces, it is required that the rotation sub-contact surfaces on the two rotation axes in the group are the same, which is set as the second mode.

[0009] Preferably, the step S1 specifically includes the following steps: In step S31, considering the characteristics of the geometry in which the rotation axis passes through the center of the regular hexagonal prism surface and the characteristics of the adjacency matrix, there are eight rotation sub-contact surfaces, and in step S23, the rotation sub-contact surfaces are rotated in the first mode. JPEG2024178885000005.jpg7170JPEG2024178885000006.jpg58170JPEG2024178885000007.jpg34170JPEG2024178885000008.jpg47123JPEG2024178885000009.jpg7170 is the lth related parameter where the turning sub-contact surface intersects, where l is a constant and has a value of 1 to 6.

[0010] Preferably, the step S4 specifically includes the following steps: JPEG2024178885000010.jpg61700 or 1 to obtain spatial Rubik's Cube mechanisms for different topology configurations. JPEG2024178885000011.jpg6170 When the turning sub-contact surfaces at the group rotation axis are the same and the turning sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel, a first type of topological configuration for the spatial Rubik's Cube mechanism is obtained in a first embodiment. JPEG2024178885000012.jpg7170 When the turning sub-contact surfaces at the group rotation axis are different and the turning sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel, a second type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000013.jpg6170 When the turning sub-contact surfaces at the group rotation axis are different and the turning sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel, a third type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000014.jpg6170 When the rotation sub-contact surfaces at the top rotation axis are different and the rotation sub-contact surfaces at the top rotation axis and the bottom rotation axis are parallel, a fourth type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000015.jpg6170 When the rotation sub-contact surfaces at the top rotation axis are the same and the rotation sub-contact surfaces at the top rotation axis and the bottom rotation axis are parallel, a fifth type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000016.jpg6170 When the rotating sub-contact surfaces are the same at the group rotation axis and the rotating sub-contact surfaces at the upper rotation axis and the lower rotation axis are concave inward, a sixth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000017.jpg6170 When the rotating sub-contact surfaces are the same at the group rotation axis and the rotating sub-contact surfaces at the upper rotation axis and the lower rotation axis are concave inward, a seventh type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000018.jpg6170 When the rotating sub-contact surfaces are different at the group rotation axis and the rotating sub-contact surfaces are concave inward at the upper rotation axis and the lower rotation axis, an eighth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. JPEG2024178885000019.jpg6170 When the rotation sub-contact surfaces are different at the group rotation axis and the rotation sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis, a ninth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. When the rotation sub-contact surfaces are the same at the group rotation axis of JPEG2024178885000020.jpg6170 and the rotation sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis, a tenth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. By combining the JPEG2024178885000021.jpg6170 values ​​with 0 or 1, we obtain spatial Rubik's Cube mechanisms for different topological configurations. When the rotation sub-contact surfaces are different on the three group rotation axes and the rotation sub-contact surfaces on the upper rotation axis and the lower rotation axis are parallel, a first type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the second aspect. When the rotation sub-contact surfaces at the three group rotation axes are different and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel, a second type of topology configuration for the spatial Rubik's Cube mechanism in a second aspect is obtained. When the rotation sub-contact surfaces at the three group rotation axes are different and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel, a third type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the second aspect. When the rotation sub-contact surfaces are different at the group rotation axis of JPEG2024178885000025.jpg6170 and the rotation sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis, a fourth type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the second aspect. When the rotation sub-contact surfaces are different at the group rotation axis of JPEG2024178885000026.jpg6170 and the rotation sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis, a fifth type of topological configuration for the spatial Rubik's Cube mechanism is obtained in the second aspect. When the rotation sub-contact surfaces are the same on the three group rotation axes and the rotation sub-contact surfaces are parallel on the upper rotation axis and the lower rotation axis, a sixth type of topology configuration for the spatial Rubik's Cube mechanism in the second aspect is obtained.

[0011] Preferably, the step S5 specifically includes the following steps: Step S51 is to select the intersection line of the rotating sub-contact surface on the top surface while taking into account the symmetry of the regular hexagonal prism based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment in step S415, and to execute step S52, and to select the intersection line of the rotating sub-contact surface on the side surface. Step S52 considers the symmetry of the regular hexagon on the top surface of the regular hexagonal prism, and selects six vertices and midpoints of six sides of the regular hexagon to establish the symmetry of the rotation axis of the planar Rubik's Cube mechanism. Step S521 selects the connecting lines between the six vertices of the regular hexagon and the centers of each face as first straight lines that exist when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, and sets the six intersection points of the intersection lines between all the first straight lines on the top surface and all the rotating sub-contact surfaces in a manner that establishes a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism. Step S522 selects the connecting lines between the midpoints of the six sides of the regular hexagon and the centers of each face as second straight lines that exist when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, and sets the six intersection points of the intersection lines between all the second straight lines on the top surface and all the rotating sub-contact surfaces in a manner that establishes a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism. Step S53 considers the symmetry of the side regular side of the regular hexagonal prism, and selects four vertices and midpoints of the four sides of each regular side to establish the symmetry of the rotation axis of the planar Rubik's Cube mechanism. Step S531: Select a third straight line that exists when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism by connecting the four vertices of the equilateral triangle with the centers of the faces, and set the four intersections of all the third straight lines on the top surface and all the rotating sub-contact surfaces in a manner that establishes a third type of symmetry about the rotation axis of the planar Rubik's Cube mechanism. Step S532 selects the connecting lines between the midpoints of the four sides of the regular side and the centers of each face as fourth straight lines that exist when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, and sets the four intersection points of the intersection lines between all the fourth straight lines on the top surface and all the rotating sub-contact surfaces in a manner that establishes a fourth type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0012] Preferably, the step S6 specifically includes the following steps: Step S61 adds a rotation axis at the center of the face based on a manner in which a first type of symmetry is established about the rotation axis of the planar Rubik's Cube mechanism to obtain a first type of topological configuration for the planar Rubik's Cube mechanism, and adds a rotation axis at the center of the face based on a manner in which a second type of symmetry is established about the rotation axis of the planar Rubik's Cube mechanism to obtain a second type of topological configuration for the planar Rubik's Cube mechanism. Step S62 obtains a third type of topological configuration for the planar Rubik's Cube mechanism based on the manner in which a third type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism, obtains a fourth type of topological configuration for the planar Rubik's Cube mechanism based on the manner in which a fourth type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism, and obtains a fifth type of topological configuration for the planar Rubik's Cube mechanism by combining the manner in which the third type of symmetry is installed and the manner in which the fourth type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism, and adding one rotation axis at the center of the face.

[0013] Preferably, the step S7 specifically includes the following steps: Step S71 selects a first type of topological configuration for a planar Rubik's Cube mechanism for the top and bottom surfaces of the regular hexagonal prism based on the fifth type of topological configuration for the spatial Rubik's Cube mechanism in the first embodiment in step S415, and simultaneously selects a third type of topological configuration, a fourth type of topological configuration and a fifth type of topological configuration for the planar Rubik's Cube mechanism for the six side surfaces, respectively, to obtain the first type of topological configuration, the second type of topological configuration and the third type of topological configuration for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively. Step S72 selects a second type of topology configuration for a planar Rubik's Cube mechanism for the top and bottom surfaces of the regular hexagonal prism based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment in step S415, and simultaneously selects a third type of topology configuration, a fourth type of topology configuration and a fifth type of topology configuration for the planar Rubik's Cube mechanism for the six side surfaces, respectively, to obtain the fourth type of topology configuration, the fifth type of topology configuration and the sixth type of topology configuration for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively. Effect of the Invention

[0014] Compared with the prior art, the technical advantages of the present invention are as follows: 1. The topology construction method for the space planar Rubik's Cube mechanism based on the regular hexagonal prism designed in the present invention is based on the symmetry between the rotation axis and the turning sub-contact surface of the regular hexagonal prism, and the rotation axis and the turning sub-contact surface of the space Rubik's Cube mechanism are set up, and the intersection of the turning sub-contact surface is analyzed to construct the adjacency matrix, which basically solves the problem that it is difficult to construct the space Rubik's Cube mechanism, and provides a theoretical basis for constructing the topology configuration of the space Rubik's Cube mechanism.

[0015] 2. The topology construction method for the spatial planar Rubik's Cube mechanism based on a regular hexagonal prism designed by the present invention can provide a basis for constructing the planar topology of the spatial Rubik's Cube mechanism by setting the rotation axis of the planar Rubik's Cube mechanism based on the intersection line of the turning sub-contact surface in the plane and the symmetry of the spatial Rubik's Cube mechanism, and can identify the principle for constructing the topology construction of the planar Rubik's Cube mechanism.

[0016] 3. The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism designed in this invention is based on the topology constructions of a spatial Rubik's Cube mechanism and a planar Rubik's Cube mechanism, and constructs the topology construction of a spatial planar Rubik's Cube mechanism of a regular hexagonal prism through the compatibility of the rotation axis and the turning sub-contact surface. This increases the number of forms of topology constructions for spatial Rubik's Cube mechanisms and makes the method of constructing spatial Rubik's Cube mechanisms convenient, which can lay a foundation for the research and application of Rubik's Cube topology construction. [Brief description of the drawings]

[0017] Other features, objects and advantages of the present application will become more apparent from the detailed description of the non-limiting embodiments with reference to the following drawings, in which: [Figure 1] 1 is a flow chart showing a method for constructing a topology for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism according to the present invention. [Figure 2a] FIG. 2 is a schematic diagram showing the installation of the first rotation axis for the spatial Rubik's Cube mechanism of the present invention; [Figure 2b] 1 is a schematic diagram showing the installation of a second type of rotation axis for the spatial Rubik's Cube mechanism of the present invention. [Figure 2c] 1 is a schematic diagram showing the installation of a third type of rotation axis for the spatial Rubik's Cube mechanism of the present invention. [Figure 2d] 1 is a schematic diagram showing the installation of a fourth type of rotation axis for the spatial Rubik's Cube mechanism of the present invention. [Figure 2e] 1 is a schematic diagram showing the installation of the fifth type of rotation axis for the spatial Rubik's Cube mechanism of the present invention. [Figure 2f] 1 is a schematic diagram showing the installation of the sixth type of rotation axis for the spatial Rubik's Cube mechanism of the present invention. [Figure 3a] FIG. 2 is a schematic diagram illustrating a first type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3b] FIG. 2 is a schematic diagram illustrating a second type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3c] FIG. 2 is a schematic diagram illustrating a third type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3d] FIG. 2 is a schematic diagram illustrating a fourth type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3e] FIG. 2 is a schematic diagram illustrating a fifth type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3f] FIG. 2 is a schematic diagram illustrating a sixth type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3g] FIG. 2 is a schematic diagram illustrating a seventh type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3h]FIG. 2 is a schematic diagram illustrating an eighth type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3i] FIG. 2 is a schematic diagram showing a ninth type of topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 3j] FIG. 2 is a schematic diagram showing a tenth topology for a spatial Rubik's Cube mechanism according to the first embodiment of the present invention. [Figure 4a] FIG. 2 is a schematic diagram showing a first type of topology for a spatial Rubik's Cube mechanism according to the second embodiment of the present invention. [Figure 4b] FIG. 2 is a schematic diagram illustrating a second type of topology for a spatial Rubik's Cube mechanism according to a second embodiment of the present invention. [Figure 4c] FIG. 11 is a schematic diagram illustrating a third type of topology for a spatial Rubik's Cube mechanism according to the second embodiment of the present invention. [Figure 4d] FIG. 2 is a schematic diagram illustrating a fourth type of topology for a spatial Rubik's Cube mechanism according to the second embodiment of the present invention. [Figure 4e] FIG. 11 is a schematic diagram illustrating a fifth type of topology for a spatial Rubik's Cube mechanism according to the second embodiment of the present invention. [Figure 4f] FIG. 2 is a schematic diagram illustrating a sixth type of topology for a spatial Rubik's Cube mechanism according to the second embodiment of the present invention. [Figure 5a] FIG. 2 is a schematic diagram showing how the regular hexagonal top surface of the regular hexagonal prism of the present invention is symmetrical about the rotation axis of the planar Rubik's Cube mechanism. [Figure 5b] FIG. 2 is a schematic diagram showing the establishment of symmetry about the rotation axis of a planar Rubik's Cube mechanism on the side regular side of a regular hexagonal prism according to the present invention. [Figure 6a] FIG. 2 is a schematic diagram illustrating a first type of topology for a planar Rubik's Cube mechanism according to the present invention. [Figure 6b] FIG. 2 is a schematic diagram illustrating a second type of topology for a planar Rubik's Cube mechanism according to the present invention. [Figure 7a]FIG. 2 is a schematic diagram illustrating a third type of topology for a planar Rubik's Cube mechanism according to the present invention. [Figure 7b] FIG. 2 is a schematic diagram illustrating a fourth type of topology for a planar Rubik's Cube mechanism according to the present invention. [Figure 7c] FIG. 2 is a schematic diagram illustrating a fifth type of topology for a planar Rubik's Cube mechanism according to the present invention. [Figure 8a] FIG. 2 is a schematic diagram showing a first topology configuration of the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention; [Figure 8b] FIG. 2 is a schematic diagram illustrating a second type of topology for the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention. [Figure 8c] FIG. 2 is a schematic diagram illustrating a third type of topology for the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention. [Figure 8d] FIG. 2 is a schematic diagram illustrating a fourth type of topology for the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention. [Figure 8e] FIG. 13 is a schematic diagram illustrating a fifth type of topology for the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention. [Figure 8f] FIG. 13 is a schematic diagram illustrating a sixth type of topology for the regular hexagonal prism space planar Rubik's Cube mechanism according to the present invention. [Figure 9a] FIG. 2 is a schematic diagram showing the configuration of a first type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 9b] FIG. 13 is a schematic diagram showing the configuration of a second type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 9c] FIG. 11 is a schematic diagram showing the configuration of a third type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 9d]FIG. 11 is a schematic diagram showing the configuration of a fourth type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 9e] FIG. 11 is a schematic diagram showing the configuration of a fifth type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 9f] FIG. 11 is a schematic diagram showing the configuration of a sixth type of rotation axis for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 10a] FIG. 2 is a schematic diagram illustrating a first topology of a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 10b] FIG. 2 is a schematic diagram illustrating a second type of topology for a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 10c] FIG. 13 is a schematic diagram illustrating a third type of topology for a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 10d] FIG. 11 is a schematic diagram showing a fourth type of topology for a regular hexagonal prism-based space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 10e] FIG. 11 is a schematic diagram illustrating a fifth type of topology for a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 11] 13 is a schematic diagram showing the symmetry of the rotation axis of a planar Rubik's Cube mechanism for a regular hexagonal prism on the upper surface of the regular hexagonal prism in another specific embodiment of the present invention. [Figure 12a] FIG. 2 is a schematic diagram illustrating a first type of topology for a planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 12b] FIG. 13 is a schematic diagram illustrating a second type of topology for a planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 12c]FIG. 11 is a schematic diagram illustrating a third type of topology for a planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 13a] FIG. 2 is a schematic diagram illustrating a first topology of a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 13b] FIG. 2 is a schematic diagram illustrating a second type of topology for a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. [Figure 13c] FIG. 13 is a schematic diagram illustrating a third type of topology for a regular hexagonal prism-shaped space planar Rubik's Cube mechanism according to another specific embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] The present application will be described in more detail with reference to the drawings and examples below. It is to be understood that the specific examples mentioned herein are not intended to limit the invention, but are merely intended to interpret the related invention. Furthermore, for the sake of convenience, only parts related to the invention are shown in the drawings.

[0019] It should be noted that, unless there is a contradiction, the features described in the embodiments and the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the embodiments and drawings.

[0020] 1 shows a topology construction method for a space planar Rubik's Cube mechanism based on a regular hexagonal prism according to the present invention. The method includes the following steps:

[0021] Step S1: Set the rotation axis of the spatial Rubik's Cube mechanism based on the symmetry of the rotation axis of the regular hexagonal prism. Select the center point of the regular hexagonal prism as the intersection point of all the rotation axes, and set the rotation axis of the spatial Rubik's Cube mechanism based on the position of the feature point on the rotation axis.

[0022] Step S11 obtains a first kind of rotation axis setting for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the centers of the regular hexagonal prism faces respectively, as shown in FIG. 2a.

[0023] Step S12 obtains a second type of rotation axis setting for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the vertices of the regular hexagonal prisms respectively, as shown in FIG. 2b.

[0024] Step S13 obtains a third type of rotation axis configuration for the spatial Rubik's Cube mechanism when the feature points on the rotation axis simultaneously pass through the midpoints of the sides of the regular hexagonal prism respectively, as shown in FIG. 2c.

[0025] Step S14 obtains a fourth type of rotation axis setting for the spatial Rubik's Cube mechanism when the characteristic point on the rotation axis partially passes through the center of the regular hexagonal prism face and partially passes through the apex of the regular hexagonal prism, as shown in FIG. 2d.

[0026] Step S15, as shown in FIG. 2e, obtains a fifth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis partly pass through the vertex of the regular hexagonal prism and partly pass through the midpoint of the side of the regular hexagonal prism.

[0027] Step S16 obtains a sixth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis partly pass through the center of the regular hexagonal prism face and partly pass through the midpoint of the side of the regular hexagonal prism, as shown in FIG. 2f.

[0028] Step S2 sets the turning sub-contact surface of the spatial Rubik's Cube mechanism based on the symmetry of the turning sub-contact surface of the regular hexagonal prism, divides the rotation axes of the spatial Rubik's Cube mechanism into multiple groups, determines the turning angle required to overlap each group, determines the grouping into the same turning sub-contact surface, and sets the symmetry of the turning sub-contact surface of the spatial Rubik's Cube mechanism.

[0029] Step S21 is a step for setting the first type of rotation axes for the spatial Rubik's Cube mechanism obtained in step S11. If the six rotation axes are divided into six groups, step S22 is executed; if the six rotation axes are divided into two groups, step S23 is executed; if the six rotation axes are divided into three groups, step S24 is executed. The turning sub-contact surfaces on the six rotation axes simultaneously intersect with the turning sub-contact surfaces on the rotation axes that pass through the centers of both the upper and lower surfaces.

[0030] Step S22 requires that when there is only one rotation axis in each group, the rotation axes are rotated by an integer multiple of 60° to overlap, and when establishing the symmetry of the rotation sub-contact surfaces, the rotation sub-contact surfaces on the six rotation axes are the same.

[0031] Step S23, when there are three rotation axes in each group, rotates the rotation axes by an integer multiple of 120° so as to overlap, and when setting the symmetry of the rotation sub-contact surfaces, it is required that the rotation sub-contact surfaces on the three rotation axes in each group are the same, and this is set as the first mode.

[0032] Step S24, when there are two rotation axes in each group, rotates the rotation axes by an integer multiple of 180° so as to overlap, and when setting the symmetry of the rotation sub-contact surfaces, it is required that the rotation sub-contact surfaces on the two rotation axes in each group are the same, which is set as the second mode.

[0033] Step S3 is to determine a neighboring area where the turning sub-contact surfaces intersect based on the intersection of the turning sub-contact surfaces. JPEG2024178885000028.jpg7170JPEG2024178885000029.jpg38170JPEG2024178885000030.jpg19170

[0034] JPEG2024178885000031.jpg14170 If a and b are not present, the corresponding element in the adjacency matrix will be 0. Among them, a and b are two constants with different values ​​between 1 and n. If a certain column or row in the adjacency matrix is ​​both 0, the corresponding turning sub-contact surface and the turning sub-contact surface do not intersect, or there is no turning sub-contact surface and no rotation axis in this state at a certain distance. In addition, the corresponding turning sub-contact surface does not exist in the movement process of reconstructing the spatial Rubik's Cube mechanism, and the corresponding rotation axis is also considered not to exist.

[0035] In step S31, considering the characteristics of the geometry in which the rotation axis passes through the center of the regular hexagonal prism surface and the characteristics of the adjacency matrix, there are a total of eight rotation sub-contact surfaces, and in step S23, the rotation is performed in the first mode. JPEG2024178885000032.jpg7170JPEG2024178885000033.jpg58170JPEG2024178885000034.jpg14170 but the value is 1 to 5.

[0036] In step S32, in step S24, for the second embodiment, the six rotation axes passing through the center of the side surface are coplanar and uniformly distributed, and the rotation sub-contact surfaces of three adjacent rotation axes are not the same. Therefore, when the rotation sub-contact surfaces of the six rotation axes intersect, even if one of the rotation axes is selected and rotated, it is not possible to rotate around any one of the six rotation axes. Therefore, in order to complete the movement that reconstitutes the spatial Rubik's Cube mechanism, the rotation sub-contact surfaces of the rotation axes that passed through the centers of the upper and lower surfaces in the second embodiment must simultaneously intersect with the six rotation axes that passed through the centers of the side surfaces. Therefore, in step S24, the second embodiment in which the rotation sub-contact surfaces intersect in the second embodiment is selected. JPEG2024178885000035.jpg7170JPEG2024178885000036.jpg57170JPEG2024178885000037.jpg7170This is the lth related parameter where the sub-contact surfaces intersect, where l is a constant and has a value between 1 and 6.

[0037] Step S4 constructs a topology configuration for the spatial Rubik's Cube mechanism based on the adjacency matrix. In order to ensure that there is a valid turning sub-contact surface for each rotation axis in a certain distribution of rotation axes, it is necessary to ensure that the row or column in which the turning sub-contact surface is located in the adjacency matrix is ​​not all zero. By combining the values ​​of multiple related parameters with 0 or 1 in the adjacency matrix where the turning sub-contact surface intersects, a spatial Rubik's Cube mechanism with a different topology configuration is obtained.

[0038] Step S41 is a step of adding the first adjacent matrix in step 31 as shown in FIGS. JPEG2024178885000038.jpg34170

[0039] JPEG2024178885000039.jpg7170, when the turning sub-contact surfaces of the two groups of rotation axes on the side are the same and the turning sub-contact surfaces of the top rotation axis and the bottom rotation axis are parallel, a first kind of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment. At the same time, the same turning sub-contact surfaces of the rotation axes in the same group do not intersect, so that the spatial Rubik's Cube mechanism is formed by the rotation axes passing through the centers of the top and bottom faces. JPEG2024178885000040.jpg7170. Since the rotation sub-contact surface on the rotation axis is the same, after rotating an integer multiple of 60° around the rotation axis passing through the center of the upper and lower surfaces, it can be subsequently rotated around any one of the eight rotation axes. Of course, after first rotating an integer multiple of 180° around the rotation axis passing through the center of the side surface, it may be subsequently rotated around any one of the eight rotation axes.

[0040] JPEG2024178885000041.jpg6170, the first embodiment obtains a second kind of topology configuration for the spatial Rubik's Cube mechanism when the rotation axes of the two groups on the side are different and the rotation axes of the upper and lower rotation axes are parallel. In this case, the same rotation sub-contact surfaces on the rotation axes of the same group do not intersect. JPEG2024178885000042.jpg7170 must be rotated an integer multiple of 120°, otherwise it cannot be rotated around any one of the eight rotation axes.

[0041] JPEG2024178885000043.jpg7170, when the rotation sub-contact surfaces at the two side groups of rotation axes are different and the rotation sub-contact surfaces at the top and bottom rotation axes are parallel, a third type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment, in which the rotation sub-contact surfaces intersect at the rotation axis of one of the groups.

[0042] JPEG2024178885000044.jpg6170 The fourth kind of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment when the turning sub-contact surfaces are different at the two group rotation axes in the plane and the turning sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis. In this case, the turning sub-contact surfaces at the two group rotation axes intersect with each other. Obviously, the more the turning sub-contact surfaces intersect, the more complicated the topology configuration of the Rubik's Cube mechanism formed will be.

[0043] JPEG2024178885000045.jpg6170 surface is filled with the same turning sub-contact surface at the two group rotation axes and parallel turning sub-contact surface at the top and bottom rotation axes, the first embodiment obtains the fifth kind of topology configuration for the spatial Rubik's Cube mechanism. In this case, the turning sub-contact surfaces at the two group rotation axes intersect together. The spatial Rubik's Cube mechanism is more symmetrical than the one shown in FIG. 3d, so that there are more combinations in the end.

[0044] JPEG2024178885000046.jpg6170, when the turning sub-contact surfaces on the two groups of rotation axes on the side are the same and the turning sub-contact surfaces on the upper and lower rotation axes are concave inward, a sixth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment, in which the turning sub-contact surfaces on the rotation axis passing through the centers of the upper and lower faces partially intersect with the turning sub-contact surfaces on the two groups of rotation axes passing through the centers of the side faces, while the turning sub-contact surfaces on the rotation axis of the same group passing through the center of the side faces do not intersect.

[0045] JPEG2024178885000047.jpg6170, when the turning sub-contact surfaces on the two groups of rotation axes on the side are the same and the turning sub-contact surfaces on the upper and lower rotation axes are concave inward, the seventh type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment, in which the turning sub-contact surfaces on the rotation axes passing through the centers of the upper and lower surfaces and the turning sub-contact surfaces on the two groups of rotation axes passing through the centers of the side surfaces partially intersect, while the first groups between the turning sub-contact surfaces on the rotation axes of the same group passing through the centers of the side surfaces intersect.

[0046] JPEG2024178885000048.jpg7170, when the turning sub-contact surfaces on the two groups of rotation axes on the side are different and the turning sub-contact surfaces on the upper rotation axis and the lower rotation axis are recessed inward, the eighth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment is obtained, in which the turning sub-contact surfaces on the rotation axis passing through the center of the upper and lower surfaces and the turning sub-contact surfaces on the two groups of rotation axes passing through the center of the side partially intersect, while the second group between the turning sub-contact surfaces on the rotation axis of the same group passing through the center of the side intersect.

[0047] Due to the relative simplicity and symmetry of the sixth type of topology configuration shown in FIG. 3f, the seventh and eighth types of topology configurations shown in FIGS. 3g and 3h are essentially the same.

[0048] JPEG2024178885000049.jpg6170, when the turning sub-contact surfaces of the two groups of rotation axes on the side are different and the turning sub-contact surfaces of the upper rotation axis and the lower rotation axis are parallel, the ninth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment, in which the turning sub-contact surfaces of the rotation axis passing through the center of the upper and lower faces intersect with the turning sub-contact surfaces of the two groups of rotation axes passing through the center of the side, and the turning sub-contact surfaces of the different groups of rotation axes on the rotation axis passing through the center of the side do not intersect.

[0049] JPEG2024178885000050.jpg7170, the tenth topological configuration for the spatial Rubik's Cube mechanism is obtained in the first embodiment when the rotation sub-contact surfaces of the two groups of rotation axes on the side are the same and the rotation sub-contact surfaces of the upper rotation axis and the lower rotation axis are parallel. In this case, the rotation sub-contact surfaces of the rotation axis passing through the center of the upper and lower surfaces intersect with the rotation sub-contact surfaces of the two groups of rotation axes passing through the center of the side, and the rotation sub-contact surfaces of the rotation axes of different groups on the rotation axis passing through the center of the side do not intersect.

[0050] Compared with the previous eight topology configurations, the ninth and tenth topology configurations of the spatial Rubik's Cube mechanism in the first embodiment are relatively simple, and the number of exchangeable means is obviously less. Among them, the tenth topology configuration of the spatial Rubik's Cube mechanism in the first embodiment has a higher symmetry than the ninth topology configuration, and therefore has more final combination states.

[0051] Step S42 is a step of dividing the second adjacency matrix in step 32 into two parts, as shown in FIGS. This is the turning sub-contact surface of JPEG2024178885000051.jpg28170.

[0052] JPEG2024178885000052.jpg14170 A first kind of transformation for the spatial Rubik's Cube mechanism in the second embodiment is performed when the contact surfaces are different and the rotation sub-contact surfaces are parallel to each other at the upper and lower rotation axes. JPEG2024178885000053.jpg38170By selecting two rotation axes that are collinear and sequentially repeating the above rotation operation, the movement that reconstructs the Rubik's Cube mechanism is realized.

[0053] JPEG2024178885000054.jpg6170, when the three group rotation axes on the side are different in the turning sub-contact surface, and the upper and lower rotation axes are parallel in the turning sub-contact surface, the second type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the second mode. In this case, the turning sub-contact surface on each group rotation axis intersects. It obviously has good symmetry. The turning operation of the spatial Rubik's Cube mechanism can not only be fulfilled as shown in FIG. 4a, but also realized that when the turning angle of the rotation axis around the center of the side is turned by an integer multiple of 60°, it is turned around the rotation axis passing through the center of the upper and lower surfaces. It is obvious that the spatial Rubik's Cube mechanism has many motion states to be reconfigured, and thus has more combination states, as shown in FIG. 4b.

[0054] JPEG2024178885000055.jpg6170, when the three groups of rotation axes on the side are different and the rotation sub-contact surfaces on the top and bottom rotation axes are parallel, a third kind of topology configuration for the spatial Rubik's Cube mechanism in the second embodiment is obtained. In this case, the rotation sub-contact surfaces intersect at the rotation axis located at one rotation axis according to Fig. 4b. Since more rotation sub-contact surfaces intersect, it has a more complicated topology configuration than the spatial Rubik's Cube mechanism shown in Fig. 4a.

[0055] JPEG2024178885000056.jpg6170, when the turning sub-contact surfaces are different in the three groups rotation axes on the side and the turning sub-contact surfaces are parallel in the upper and lower rotation axes, a fourth kind of topological configuration for the spatial Rubik's Cube mechanism is obtained in the second embodiment. It is obvious that the spatial Rubik's Cube mechanism has a more complicated topological configuration and has more interchangeable means than the two spatial Rubik's Cube mechanisms shown in Fig. 4b and Fig. 4c.

[0056] When the rotation sub-contact surfaces of the three groups of rotation axes on the side are different and the rotation sub-contact surfaces of the upper and lower rotation axes are parallel, a fifth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the second embodiment, in which the rotation sub-contact surfaces of the rotation axes passing through the center of the side do not intersect, and only the rotation sub-contact surfaces of the rotation axes passing through the center of the upper surface and the lower base intersect.

[0057] When the rotation sub-contact surfaces of the three groups of rotation axes on the side are the same and the rotation sub-contact surfaces of the upper and lower rotation axes are parallel, a sixth type of topology configuration for the spatial Rubik's Cube mechanism is obtained in the second embodiment. In this case, the rotation sub-contact surfaces of the rotation axes passing through the centers of the side faces partially intersect, and the rotation sub-contact surfaces of the rotation axes passing through the centers of the upper and lower faces intersect.

[0058] In order to obtain Rubik's Cube mechanisms with more topological configurations, a comprehensive method is provided to obtain compatibility with the spatial planar Rubik's Cube by combining the obtained spatial Rubik's Cube mechanisms with planar Rubik's Cube mechanisms of different topological configurations. The overall idea of ​​the method is to take the planar Rubik's Cube mechanism as a module and combine it with the spatial Rubik's Cube mechanism to obtain a spatial planar Rubik's Cube mechanism.

[0059] Step S5: set the rotation axis of the planar Rubik's Cube according to the intersection line of the turning sub-contact surface and the symmetry of the spatial Rubik's Cube mechanism. According to the spatial Rubik's Cube mechanisms with different topological configurations, select the intersection lines of the turning sub-contact surfaces on different planes in the spatial Rubik's Cube mechanism to set the symmetry of the rotation axis of the planar Rubik's Cube.

[0060] Step S51 is a step in which, based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism under the first aspect in step S415, while taking into account the symmetry of the regular hexagonal prism, an intersection line of the rotating sub-contact surface on the top surface is selected to perform step S52, and an intersection line of the rotating sub-contact surface on the side surface is selected to perform step S53.

[0061] Step S52 considers the symmetry of the regular hexagon on the top surface of the regular hexagonal prism, and selects six vertices and midpoints of six sides of the regular hexagon to establish symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0062] S521 selects the connecting lines between the six vertices of the regular hexagon and the centers of each face as the first straight line that exists when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, in accordance with the first straight line that exists when establishing symmetry about the rotation axis of the planar Rubik's Cube shown in Figure 5a and the first mode of establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, and sets the six intersection points of the intersection lines between all the first straight lines on the top surface and all the turning sub-contact surfaces in a mode of establishing a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0063] Step S522 selects the connecting lines between the midpoints of the six sides of the regular hexagon and the centers of each face as the second straight line existing when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, in accordance with the second straight line existing when establishing symmetry about the rotation axis of the planar Rubik's Cube shown in Figure 5a, and sets the six intersection points of the intersection lines between all the second straight lines on the top surface and all the turning sub-contact surfaces as a mode of establishing a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0064] Step S53 considers the symmetry of the side regular side of the regular hexagonal prism, and selects four vertices and midpoints of the four sides of the regular side to establish symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0065] Step S531 selects the connecting lines between the four vertices of the equilateral side and the centers of each face as third straight lines when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, in the same manner as the first manner of establishing symmetry about the rotation axis of the planar Rubik's Cube and straight line 1 shown in Figure 5b, and sets the four intersection points of all the third straight lines on the top surface and the intersection lines of all the rotating sub-contact surfaces as a manner of establishing a third type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0066] Step S532 selects the connecting lines between the midpoints of the four sides of the equilateral side and the centers of each face as fourth straight lines existing when establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, in accordance with line 2 existing when establishing symmetry about the rotation axis of the planar Rubik's Cube shown in Figure 5b and the second mode of establishing symmetry about the rotation axis of the planar Rubik's Cube mechanism, and sets the four intersection points of the intersection lines of all fourth straight lines on the top surface and all turning sub-contact surfaces as a mode of establishing a fourth type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

[0067] Step S6 constructs a topological configuration for the planar Rubik's Cube mechanism by establishing the symmetry of the rotation axis of the planar Rubik's Cube.

[0068] Step S61, as shown in Fig. 6a, adds a rotation axis at the center of the face based on the manner of setting a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism to obtain a first type of topology configuration for the planar Rubik's Cube mechanism, and as shown in Fig. 6b, adds a rotation axis at the center of the face based on the manner of setting a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism to obtain a second type of topology configuration for the planar Rubik's Cube mechanism. Both the first type and the second type of topology configuration for the planar Rubik's Cube mechanism can rotate around any one rotation axis by an integer multiple of 60°, and then rotate around the remaining rotation axis. JPEG2024178885000059.jpg8170 For the topology configuration, the y-th rotation axis is located on the plane where the 7th rotation axis is located, where x is a constant with a value of 1 to 2, and y is a constant with a value of 1 to 7.

[0069] Step S62 obtains a third type of topology configuration for the planar Rubik's Cube mechanism based on the manner in which a third type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism as shown in Fig. 7a, and obtains a fourth type of topology configuration for the planar Rubik's Cube mechanism based on the manner in which a fourth type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism as shown in Fig. 7b. As shown in Fig. 7c, based on the manner in which the third type of symmetry is installed about the rotation axis of the planar Rubik's Cube mechanism and the manner in which the fourth type of symmetry is installed, a fifth type of topology configuration for the planar Rubik's Cube mechanism is obtained by adding a rotation axis at the center of the face. The third type, fourth type and fifth type of topology configuration for the planar Rubik's Cube mechanism all rotate an integer multiple of 90° around any of the rotation axes, and then rotate the remaining number of times. In the case of 71705 types of JPEG2024178885000060.jpg, the qth rotation axis is located on the plane where the 1st rotation axis is located in the pth type of topology configuration, where p is a constant and has a value of 3 to 4, and q is a constant and has a value of 1 to 4.

[0070] Step S7 constructs a topological configuration for a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism based on the spatial Rubik's Cube mechanism and the planar Rubik's Cube mechanism. By using the spatial Rubik's Cube mechanisms of the multiple topological configurations obtained in step S4 and the multiple topologically constructed planar Rubik's Cube mechanisms obtained in step S6, a regular hexagonal prism-shaped spatial planar Rubik's Cube mechanism with different topological configurations is obtained.

[0071] Step S71, as shown in Figures 8a, 8b and 8c, selects a first type of topology configuration for a planar Rubik's Cube mechanism for the top and bottom surfaces of a regular hexagonal prism based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment in step S415, and simultaneously selects a third type of topology configuration, a fourth type of topology configuration and a fifth type of topology configuration for the planar Rubik's Cube mechanism for the six side surfaces, respectively, to obtain the first type of topology configuration, the second type of topology configuration and the third type of topology configuration for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively.

[0072] Step S72, as shown in Figures 8d, 8e and 8f, selects a second type of topology configuration for a planar Rubik's Cube mechanism for the top and bottom surfaces of the regular hexagonal prism based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment in step S415, and simultaneously selects a third type of topology configuration, a fourth type of topology configuration and a fifth type of topology configuration for the planar Rubik's Cube mechanism for the six side surfaces, respectively, to obtain the fourth type of topology configuration, the fifth type of topology configuration and the sixth type of topology configuration for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively.

[0073] The present invention further includes a regular hexagonal prism space planar Rubik's Cube mechanism obtained according to the above method, which has one or more of a first kind of topology configuration, a second kind of topology configuration, a third kind of topology configuration, a fourth kind of topology configuration, a fifth kind of topology configuration, or a sixth kind of topology configuration, and a regular hexagonal prism space planar Rubik's Cube mechanism with different topology configurations is obtained by selecting a combination of different topology configurations on different sides.

[0074] According to the above description of the planar Rubik's Cube mechanism, it is possible to obtain the turning characteristic of the spatial Rubik's Cube mechanism of the regular hexagonal prism based on the turning characteristic of the spatial Rubik's Cube mechanism of the regular hexagonal prism. In the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, when the planar Rubik's Cube mechanism of each upper surface and each lower surface is turned by an integer multiple of 60°, and the planar Rubik's Cube mechanism of each side surface is turned by an integer multiple of 90°, the spatial planar Rubik's Cube mechanism of the regular hexagonal prism still has the turning characteristic of the fifth kind of topology configuration (for example, as shown in FIG. 3e) for the spatial Rubik's Cube mechanism in the first embodiment according to step S415.

[0075] In addition to the multiple topology configurations for the spatial planar Rubik's Cube mechanism of a regular hexagonal prism listed above, by adopting a method of combining the above-mentioned planar Rubik's Cube mechanism and the spatial Rubik's Cube mechanism with each other, it is possible to obtain even more spatial planar Rubik's Cube mechanisms of a regular hexagonal prism with different topology configurations, but this will not be described repeatedly here.

[0076] The spatial planar Rubik's Cube mechanical topology construction method provided by the present invention can be applied to regular polyhedrons including regular hexagonal prisms, such as regular hexagonal prisms and regular octahedrons.

[0077] The method for constructing a topology according to the present invention based on the regular hexagonal prism space planar Rubik's Cube mechanism will be described in more detail below. Specifically, as shown in Fig. 9a to 13c, according to another specific embodiment of the present invention, the present invention further provides a method for constructing a topology based on the regular hexagonal prism space planar Rubik's Cube mechanism, which specifically includes the following steps:

[0078] Step S1: The rotation axis of the spatial Rubik's Cube mechanism is arranged based on the symmetry of the rotation axis of the regular hexagonal prism. The center point of the regular hexagonal prism is selected as the intersection point of all the rotation axes, and the rotation axis of the spatial Rubik's Cube mechanism is arranged according to the position of the characteristic point on the rotation axis.

[0079] As shown in FIG. 9a, when the characteristic points of the rotation axis simultaneously pass through the center of the face of the regular hexagonal prism, a first type of rotation axis is arranged for the spatial Rubik's Cube mechanism. As shown in FIG. 9b, when the characteristic points of the rotation axis simultaneously pass through the vertices of the regular hexagonal prism, a second type of rotation axis is arranged for the spatial Rubik's Cube mechanism. As shown in FIG. 9c, when the characteristic points of the rotation axis simultaneously pass through the midpoints of the sides of the regular hexagonal prism, a third type of rotation axis is arranged for the spatial Rubik's Cube mechanism. As shown in FIG. 9d, when some of the characteristic points of the rotation axis pass through the center of the face of the regular hexagonal prism and some of the characteristic points pass through the vertices of the regular hexagonal prism, a fourth type of rotation axis is arranged for the spatial Rubik's Cube mechanism. As shown in FIG. 9e, when some of the characteristic points of the rotation axis pass through the vertices of the regular hexagonal prism and some of the characteristic points pass through the midpoints of the sides of the regular hexagonal prism, a fifth type of rotation axis is arranged for the spatial Rubik's Cube mechanism. As shown in Figure 9f, when some of the characteristic points on the rotation axis pass through the center of the face of the regular hexagonal prism and some pass through the midpoints of the sides of the regular hexagonal prism, a sixth type of rotation axis for the spatial Rubik's Cube mechanism is arranged.

[0080] Step S2 arranges the turning sub-contact surfaces of the spatial Rubik's Cube mechanism based on the symmetry of the turning sub-contact surfaces of the regular hexagonal prism, divides the rotation axes of the spatial Rubik's Cube mechanism into a plurality of groups, identifies the turning angles required for each group to be overlapped, identifies groupings with the same turning sub-contact surfaces, and arranges the symmetry of the turning sub-contact surfaces of the spatial Rubik's Cube mechanism.

[0081] Step S21: for the four rotation axes passing through the center of the side in the first type of rotation axis arrangement for the spatial Rubik's Cube mechanism obtained by step S1, if the four rotation axes are divided into four groups, step S22 is executed. If the four rotation axes are divided into two groups, step S23 is executed. The rotation sub-contact surfaces of the four rotation axes simultaneously intersect with the rotation sub-contact surfaces of the rotation axes passing through the centers of the upper and lower surfaces.

[0082] In step S22, since there is only one rotation axis per group, and the rotation axis is rotated by an integer multiple of 90° to overlap, the rotation sub-contact surfaces at the four rotation axes must be the same in order to arrange the symmetry of the rotation sub-contact surfaces.

[0083] In step S23, there are two rotation axes for each group, and when the rotation axes are rotated by an integer multiple of 180°, they become overlapped. In order to arrange the symmetry of the rotation sub-contact surfaces, it is necessary that the rotation sub-contact surfaces of the two rotation axes in each group are the same.

[0084] In step S3, the adjacent matrix with which the rotating sub-contact surface intersects is identified based on the intersection of the rotating sub-contact surface. Considering the geometric characteristics that the rotation axis passes through the center of the face of the regular hexagonal prism and the characteristics of the adjacent matrix, there are a total of six rotating sub-contact surfaces, and in step S23, the adjacent matrix with which the rotating sub-contact surface intersects is identified. JPEG2024178885000061.jpg7170JPEG2024178885000062.jpg45170JPEG2024178885000063.jpg14170 parameters, and k is a constant with a value from 1 to 6.

[0085] Step S4 constructs a topology configuration for the spatial Rubik's Cube mechanism based on the adjacency matrix. When a certain rotation axis is distributed, it is necessary to ensure that the row or column in which the turning sub-contact surface is located in the adjacency matrix is ​​not all zero, in order to ensure that a valid turning sub-contact surface exists for each rotation axis. By combining the values ​​of multiple related parameters in the adjacency matrix where the turning sub-contact surface intersects with 0 or 1, a spatial Rubik's Cube mechanism with a different topology configuration is obtained.

[0086] As shown in Figures 10a to 10e, for the adjacency matrix in step 3, JPEG2024178885000064.jpg27170This is the touch surface.

[0087] JPEG2024178885000065.jpg6170If there is only one rotation sub-contact surface, the first type of topology configuration for the spatial Rubik's Cube mechanism is obtained. In this case, the spatial Rubik's Cube mechanism can be rotated around any one of the rotation axes by an integer multiple of 180°, and then rotated around any one of the six rotation axes. Since the rotation sub-contact surfaces of each rotation axis are the same, it is also possible to rotate around any one of the rotation axes by an integer multiple of 90°, and then rotate around any one of the six rotation axes.

[0088] If there exists only one turning sub-contact surface that is a curved surface, we obtain a second kind of topological configuration for the spatial Rubik's Cube mechanism. In this case, although its appearance is different from that of Fig. 10a, it has the same topological configuration, quantity of states and turning properties, so that they can be said to be the same in the essence of spatial science.

[0089] JPEG2024178885000067.jpg6170If the rotation axes of the three groups are the same, but the rotation sub-contact surfaces are different on non-collinear rotation axes, and the rotation sub-contact surfaces intersect two by two in the three groups, a third kind of topology configuration for the spatial Rubik's Cube mechanism is obtained. In this case, the spatial Rubik's Cube mechanism can only rotate an integer multiple of 180° around any one of the rotation axes, and can realize continuous rotation operations and complete the reconfigurable movement.

[0090] JPEG2024178885000068.jpg6170If there are the same turning sub-contact surfaces on the rotation axis, but different turning sub-contact surfaces on the non-collinear rotation axis, and the turning sub-contact surfaces on the rotation axis on the upper and lower surfaces are concave inward, and the turning sub-contact surfaces in the two groups on the side both intersect with the turning sub-contact surfaces on the upper and lower surfaces, a third kind of topology configuration is obtained for the spatial Rubik's Cube mechanism. In this case, the spatial Rubik's Cube mechanism can only rotate an integer multiple of 180° around any one of the rotation axes, and can realize continuous turning operations, and end the reconfigurable movement.

[0091] JPEG2024178885000069.jpg6170If the following conditions are satisfied: there are the same turning sub-contact surfaces on two rotation axes, but the turning sub-contact surfaces on non-collinear rotation axes are different, and the turning sub-contact surfaces on the rotation axes on the upper and lower surfaces are concave inward, and the turning sub-contact surfaces in the two groups on the side do not intersect with the turning sub-contact surfaces on the upper and lower surfaces, the fourth type of topology configuration for the spatial Rubik's Cube mechanism is obtained. In this case, the spatial Rubik's Cube mechanism can only rotate around any one of the rotation axes on the side by an integer multiple of 180°, and can realize continuous turning operations and complete the reconfigurable movement.

[0092] Step S5: arrange the rotation axis of the planar Rubik's Cube according to the intersection line of the turning sub-contact surface and the symmetry of the spatial Rubik's Cube mechanism. According to the spatial Rubik's Cube mechanisms with different topological configurations, select the intersection lines of the turning sub-contact surfaces on different surfaces of the spatial Rubik's Cube mechanism to arrange the symmetry of the planar Rubik's Cube rotation axis.

[0093] In step S4, based on the first kind of topology configuration for the spatial Rubik's Cube mechanism, an intersection line of the turning sub-contact surface on any face is selected while considering the symmetry of the regular hexagonal prism.

[0094] Taking into consideration the symmetry of the regular polygon of each face of the regular hexagonal prism, the four vertices of the top face and the midpoints of the four sides of the regular polygon are selected to arrange the symmetry of the rotation axis of the planar Rubik's Cube mechanism.

[0095] If the connecting lines between the four vertices of the regular polygon and the centers of each face are selected as first lines that arrange the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and all of the first lines and the four intersection points where all of the rotating sub-contact surfaces intersect with the top surface are placed in a manner that arranges a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, the result will be the line 1 that arranges the symmetry of the rotation axis of the planar Rubik's Cube in Figure 11 and the first manner that arranges the symmetry of the rotation axis of the planar Rubik's Cube.

[0096] If the connecting lines between the midpoints of the four sides of the regular polygon and the center of each face are selected as second lines that arrange the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and all of the second lines and the four intersection points where all of the rotating sub-contact surfaces intersect with the top surface are placed in a manner that arranges a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, the result will be line 2 that arranges the symmetry of the rotation axis of the planar Rubik's Cube in Figure 11 and the second manner that arranges the symmetry of the rotation axis of the planar Rubik's Cube.

[0097] When all of the first straight lines and the four intersection points where all of the rotating sub-contact surfaces intersect with the top surface and the midpoints of the centers of each face are arranged in a manner that arranges a third type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, it will become as shown in the third manner of symmetry arrangement about the rotation axis of the planar Rubik's Cube in Figure 11.

[0098] Step S6 constructs a topological configuration of the planar Rubik's Cube mechanism by arranging the symmetry of the rotation axis of the planar Rubik's Cube.

[0099] A first kind of topological configuration for a planar Rubik's Cube mechanism is obtained by arranging a first kind of symmetry about the rotation axis of the planar Rubik's Cube mechanism, as shown in FIG. 12a. A second kind of topological configuration for a planar Rubik's Cube mechanism is obtained by arranging a second kind of symmetry about the rotation axis of the planar Rubik's Cube mechanism, as shown in FIG. 12b. A third kind of topological configuration for a planar Rubik's Cube mechanism is obtained by arranging a third kind of symmetry about the rotation axis of the planar Rubik's Cube mechanism, as shown in FIG. 12c. Both the first kind of topological configuration and the second kind of topological configuration for a planar Rubik's Cube mechanism can be rotated by an integer multiple of 90° about any one of the rotation axes and then rotated about the remaining rotation axis.

[0100] Step S7 constructs a topological configuration for a spatial planar Rubik's Cube mechanism of a regular hexagonal prism based on the spatial Rubik's Cube mechanism and the planar Rubik's Cube mechanism. By combining the spatial Rubik's Cube mechanisms for the multiple topological configurations obtained in step S4 and the planar Rubik's Cube mechanisms for the multiple topological configurations obtained in step S6, a spatial planar Rubik's Cube mechanism of a regular hexagonal prism with a different topological configuration is obtained.

[0101] As shown in Fig. 13a, in step S4, based on the first kind of topology configuration for the spatial Rubik's Cube mechanism, for each face of the regular hexagonal prism, a first kind of topology configuration for the planar Rubik's Cube mechanism is selected, so as to obtain a first kind of topology configuration for the spatial planar Rubik's Cube mechanism of a regular hexagonal prism. As shown in Fig. 13b, when a second kind of topology configuration for the planar Rubik's Cube mechanism is selected, for each face of the regular hexagonal prism, a second kind of topology configuration for the spatial planar Rubik's Cube mechanism of a regular hexagonal prism is obtained. As shown in Fig. 13c, when a third kind of topology configuration for the planar Rubik's Cube mechanism is selected, for each face of the regular hexagonal prism, a third kind of topology configuration for the spatial planar Rubik's Cube mechanism of a regular hexagonal prism is obtained.

[0102] Compared with the spatial planar Rubik's Cube mechanism of a regular hexagonal prism, the topology construction method based on the spatial planar Rubik's Cube mechanism of a regular hexagonal prism according to the present invention has beneficial technical effects as follows: For a regular hexagonal prism, each face of the regular hexagonal prism has a high degree of symmetry, and the topology construction of the spatial planar Rubik's Cube mechanism obtained through the designed topology construction method has more colorful changes and can have better reconfigurable motion. According to the construction principle of the adjacency matrix and the topology construction of the planar Rubik's Cube mechanism, the top, bottom and side faces can be fully called to cooperate and combine, thereby creating a spatial planar Rubik's Cube mechanism with excellent reconfigurable performance.

[0103] The topology construction method for the spatial planar Rubik's Cube mechanism based on the regular hexagonal prism designed by the present invention sets the rotation axis and the turning sub-contact surface in the spatial Rubik's Cube mechanism according to the symmetry between the rotation axis and the turning sub-contact surface of the regular hexagonal prism, and constructs the adjacency matrix by analyzing the intersection of the turning sub-contact surface. And it can basically solve the problem that it is difficult to construct the spatial Rubik's Cube mechanism. It can provide a theoretical basis for constructing the topology construction of the spatial Rubik's Cube mechanism. By setting the rotation axis of the planar Rubik's Cube mechanism according to the symmetry between the intersection line of the turning sub-contact surface in the plane and the spatial Rubik's Cube mechanism, it can provide a basis for constructing the planar topology for the spatial Rubik's Cube mechanism, and can identify the principle of constructing the topology construction of the planar Rubik's Cube mechanism. Based on the topology configurations of the space Rubik's Cube mechanism and the planar Rubik's Cube mechanism, the topology configuration of the space planar Rubik's Cube mechanism of the regular hexagonal prism is constructed through the compatibility of the rotation axis and the turning sub-contact surface, so that the form of the topology configuration of the space Rubik's Cube mechanism is increased, and a method for constructing the space Rubik's Cube mechanism is created. This can lay a foundation for the research and application of the topology configuration of the Rubik's Cube.

[0104] In constructing the topology configuration of the regular hexagonal prism space planar Rubik's Cube mechanism of the present invention, two important steps are paid attention to. One is to determine the adjacent matrix of the turning sub-contact surface based on the intersection of the turning sub-contact surface. The other is to set the rotation axis of the planar Rubik's Cube based on the intersection line of the turning sub-contact surface and the symmetry of the space Rubik's Cube mechanism. The method of the present invention not only better meets the needs from different topology configurations, but also enriches the means of design and research on Rubik's Cube.

[0105] Finally, it should be noted that the above embodiments are for illustrating the technical means of the present invention, and are not intended to be limiting. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still amend the present invention or make equivalent substitutions. Any amendments or local substitutions made without departing from the spirit and scope of the present invention should be included in the scope of the claims of the present invention.

Claims

1. Step S1: setting the rotation axis of the spatial Rubik's Cube mechanism based on the symmetry of the rotation axis of the regular hexagonal prism, in which the center point of the regular hexagonal prism is selected as the intersection point of all the rotation axes, and the rotation axis of the spatial Rubik's Cube mechanism is set based on the position of the feature point on the rotation axis; Step S2: setting the turning sub-contact surface of the spatial Rubik's Cube mechanism based on the symmetry of the turning sub-contact surface of the regular hexagonal prism, which includes dividing the rotation axes of the spatial Rubik's Cube mechanism into multiple groups, determining the turning angle required to overlap each group, determining the grouping into the same turning sub-contact surface, and setting the symmetry of the turning sub-contact surface of the spatial Rubik's Cube mechanism; If the turning sub-contact surfaces do not intersect, the elements in the corresponding positions in the adjacency matrix are 0, among which, a and b are both constants but are two different constants with values ​​between 1 and n, and if a column or row in the adjacency matrix is ​​both 0, the corresponding turning sub-contact surface does not intersect with any of the turning sub-contact surfaces, or is spaced at a certain distance from them, in this case there is no turning sub-contact surface and no rotation axis; step S3; Step S4 of constructing a topological configuration for the spatial Rubik's Cube mechanism based on the adjacency matrix, in which the values ​​of multiple related parameters in the adjacency matrix where the turning sub-contact surfaces intersect are combined with 0 or 1 to obtain spatial Rubik's Cube mechanisms with different topological configurations; Step S5: setting the rotation axis of the planar Rubik's Cube according to the intersection line of the turning sub-contact surface and the symmetry of the spatial Rubik's Cube mechanism, in which the intersection line of the turning sub-contact surface is selected on different surfaces of the spatial Rubik's Cube mechanism according to the spatial Rubik's Cube mechanisms with different topological configurations to set the symmetry of the rotation axis of the planar Rubik's Cube; Step S6: constructing a topology configuration for the planar Rubik's Cube mechanism by establishing the symmetry of the rotation axis of the planar Rubik's Cube; Step S7: constructing a topology configuration for a spatial planar Rubik's Cube mechanism of a regular hexagonal prism using the spatial Rubik's Cube mechanism and the planar Rubik's Cube mechanism, in which the spatial Rubik's Cube mechanisms of the plurality of topology configurations obtained in step S4 and the planar Rubik's Cube mechanisms of the plurality of topology configurations obtained in step S6 are combined to obtain a spatial planar Rubik's Cube mechanism of a regular hexagonal prism having a different topology configuration; A topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism, comprising:

2. The step S1 includes: Step S11: obtaining a first type of rotation axis configuration for the spatial Rubik's Cube mechanism when the feature points on the rotation axis pass through the center of the face of the regular hexagonal prism at the same time; Step S12: obtaining a second type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis pass through the vertices of the regular hexagonal prism simultaneously; Step S13: obtaining a third type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points on the rotation axis simultaneously pass through the midpoints of the sides of the regular hexagonal prism; Step S14: obtaining a fourth type of rotation axis for the spatial Rubik's Cube mechanism when the characteristic points of the rotation axis pass through the center of the regular hexagonal prism face and pass through the apex of the regular hexagonal prism; Step S15: obtaining a fifth type of rotation axis configuration for the spatial Rubik's Cube mechanism when the characteristic points of the rotation axis pass through the vertices of the regular hexagonal prism and pass through the midpoints of the sides of the regular hexagonal prism; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, characterized in that it includes a step S16 of obtaining the establishment of a sixth type of rotation axis for the spatial Rubik's Cube mechanism when a characteristic point on the rotation axis passes partly through the center of the face of the regular hexagonal prism and partly through the midpoint of the side of the regular hexagonal prism.

3. Step 2 includes: In the spatial Rubik's Cube mechanism obtained in step S11, for the six rotation axes passing through the center of the side in the setting of the first type of rotation axes, if the six rotation axes are divided into six groups, step S22 is executed; if the six rotation axes are divided into two groups, step S23 is executed; if the six rotation axes are divided into three groups, step S24 is executed; and step S21 in which the rotation sub-contact surfaces on the six rotation axes simultaneously intersect with the rotation sub-contact surfaces on the rotation axes passing through the centers of both the upper and lower surfaces; Step S22, when there is only one rotation axis in each group, rotate the rotation axis by an integral multiple of 60° so as to overlap, and when setting the symmetry of the rotation sub-contact surface, it is required that the rotation sub-contact surfaces on the six rotation axes are the same; Step S23: when the group has three rotation axes, rotate the rotation axes by an integer multiple of 120° so as to overlap each other, and when setting the symmetry of the rotation sub-contact surface, it is necessary that the rotation sub-contact surfaces on the three rotation axes in each group are the same, and set this as the first mode; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, characterized in that it includes a step S24, in which when there are two rotation axes in each group, the rotation axes are rotated by an integer multiple of 180° so as to overlap, and when setting the symmetry of the rotation sub-contact surfaces, it is required that the rotation sub-contact surfaces on the two rotation axes in each group are the same, and this is set as the second aspect.

4. The step S1 includes: Considering the characteristics of the geometry in which the rotation axis passes through the center of the regular hexagonal prism and the characteristics of the adjacency matrix, there are a total of eight rotation sub-contact surfaces, and in step S23, the rotation sub-contact surface is In a second aspect, the topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism, as described in claim 1, further includes a step S32 in which the turning sub-contact surface intersects with the l-th relevant parameter, where l is a constant but has a value between 1 and 6.

5. The step S4 is Step S41 of obtaining a spatial Rubik's Cube mechanism for a plurality of different topology configurations by combining them in one step; Step S411: Obtain a first kind of topology configuration for the spatial Rubik's Cube mechanism in a first aspect when the rotation sub-contact surfaces are the same at the rotation axis and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; Step S412: obtaining a second type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are different at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; Step S413: obtaining a third type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are different at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; Step S414: obtaining a fourth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are different at the upper and lower rotation axes and the rotation sub-contact surfaces are parallel at the upper and lower rotation axes; Step S415: obtaining a fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are the same at the upper rotation axis and the lower rotation axis, and the rotation sub-contact surfaces are parallel at the upper rotation axis and the lower rotation axis. Step S416: obtaining a sixth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are the same at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are concave inward; Step S417: obtaining a seventh type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surface is the same at the rotation axis and the rotation sub-contact surface is concave at the upper rotation axis and the lower rotation axis; Step S418: obtaining an eighth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are different at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are concave inward; Step S419: obtaining a ninth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are different at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; Step S4110: obtaining a tenth topology configuration for the spatial Rubik's Cube mechanism in the first aspect when the rotation sub-contact surfaces are the same at the rotation axis and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; or 1 to obtain a spatial Rubik's Cube mechanism for different topological configurations; Step S421: Obtaining a first kind of topology configuration for the spatial Rubik's Cube mechanism in the second aspect when the rotation sub-contact surfaces at the top rotation axis are different and the rotation sub-contact surfaces at the top rotation axis and the bottom rotation axis are parallel; Step S422: obtaining a second type of topology configuration for the spatial Rubik's Cube mechanism in a second aspect when the rotation sub-contact surfaces at the top rotation axis are different and the rotation sub-contact surfaces at the top rotation axis and the bottom rotation axis are parallel; Step S423: obtaining a third type of topology configuration for the spatial Rubik's Cube mechanism in the second aspect when the rotation sub-contact surfaces are different at the top rotation axis and the rotation sub-contact surfaces are parallel at the top rotation axis and the bottom rotation axis. Step S424: obtaining a fourth type of topology configuration for the spatial Rubik's Cube mechanism in the second aspect when the rotation sub-contact surfaces are different at the rotation axes and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; Step S425: obtaining a fifth type of topology configuration for the spatial Rubik's Cube mechanism in the second aspect when the rotation sub-contact surfaces are different at the rotation axis and the rotation sub-contact surfaces at the upper rotation axis and the lower rotation axis are parallel; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, characterized in that the second aspect includes a step S426 of obtaining a sixth type of topology configuration for the spatial Rubik's Cube mechanism when the rotation sub-contact surfaces are the same at the top rotation axis and the rotation sub-contact surfaces are parallel at the top rotation axis and the bottom rotation axis.

6. The step S5 In step S415, based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first embodiment, while taking into account the symmetry of the regular hexagonal prism, select an intersection line of the turning sub-contact surface on the top surface and execute step S52, and select an intersection line of the turning sub-contact surface on the side surface and execute step S53; Step S52: Considering the symmetry of the regular hexagon on the top surface of the regular hexagonal prism, select six vertices and midpoints of six sides of the regular hexagon to set the symmetry of the rotation axis of the planar Rubik's Cube mechanism; Step S521: Select the connection lines between the six vertices of the regular hexagon and the centers of the faces as first straight lines that exist when establishing the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and set the six intersection points of all the first straight lines on the top surface and all the turning sub-contact surfaces to establish a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism; Step S522: Select the connecting lines between the midpoints of the six sides of the regular hexagon and the centers of the faces as second straight lines that exist when establishing the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and set the six intersections of the intersection lines of all the second straight lines and all the turning sub-contact surfaces on the upper surface to establish a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism; Step S53: Considering the symmetry of the side regular side of the regular hexagonal prism, select four vertices and midpoints of the four sides of the regular side to set the symmetry of the rotation axis of the planar Rubik's Cube mechanism; Step S531: Select the connection lines between the four vertices of the equilateral side and the centers of the faces as third straight lines that exist when establishing the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and set the four intersection points of all the third straight lines on the top surface and all the intersection lines between the rotation sub-contact surfaces to establish a third type of symmetry about the rotation axis of the planar Rubik's Cube mechanism; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, characterized in that it includes a step S532 of selecting the midpoints of the four sides of the regular side and the connecting lines between each of them and the center of the face as fourth straight lines present when establishing the symmetry of the rotation axis of the planar Rubik's Cube mechanism, and setting the four intersection points of all the fourth straight lines on the top surface and all the intersection lines between the turning sub-contact surfaces in a manner of establishing a fourth type of symmetry about the rotation axis of the planar Rubik's Cube mechanism.

7. The step S6 is Step S61: based on a mode of setting a first type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, add a rotation axis at the center of the face to obtain a first type of topology configuration for the planar Rubik's Cube mechanism; based on a mode of setting a second type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, add a rotation axis at the center of the face to obtain a second type of topology configuration for the planar Rubik's Cube mechanism; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, further comprising a step S62 of obtaining a third type of topology configuration for the planar Rubik's Cube mechanism based on a third type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, obtaining a fourth type of topology configuration for the planar Rubik's Cube mechanism based on a fourth type of symmetry about the rotation axis of the planar Rubik's Cube mechanism, and combining the third type of symmetry and the fourth type of symmetry about the rotation axis of the planar Rubik's Cube mechanism to add a rotation axis at the center of the face to obtain a fifth type of topology configuration for the planar Rubik's Cube mechanism.

8. The step S7 is Step S71: based on the fifth type of topology configuration for the spatial Rubik's Cube mechanism in the first aspect in step S415, select a first type of topology configuration for a planar Rubik's Cube mechanism for the upper and lower surfaces of the regular hexagonal prism, and simultaneously select a third type of topology configuration, a fourth type of topology configuration and a fifth type of topology configuration for the planar Rubik's Cube mechanism for each of the six side surfaces, respectively, to obtain the first type of topology configuration, the second type of topology configuration and the third type of topology configuration for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively; The topology construction method for a spatial planar Rubik's Cube mechanism based on a regular hexagonal prism as described in claim 1, characterized in that in step S415, a second type of topology construction for a planar Rubik's Cube mechanism is selected for the upper and lower surfaces of the regular hexagonal prism based on the fifth type of topology construction for the spatial Rubik's Cube mechanism in the first embodiment, and a third type of topology construction, a fourth type of topology construction and a fifth type of topology construction for the planar Rubik's Cube mechanism are simultaneously selected for each of the six side surfaces, respectively, to obtain the fourth type of topology construction, the fifth type of topology construction and the sixth type of topology construction for the spatial planar Rubik's Cube mechanism of the regular hexagonal prism, respectively.

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