Spherical surface dense paving system based on regular polygon

Abstract

The invention discloses a regular polygon-based spherical surface dense paving system which comprises a plurality of spherical surface regular polygon base bodies, the spherical surface regular polygon base bodies are based on spherical surface regular polygons, and each side edge of each spherical surface regular polygon base body is provided with a first connecting structure or a second connecting structure or the first connecting structure and the second connecting structure. The outer contour shape of the first connecting structure is matched and meshed with the outer contour shape of the second connecting structure, the multiple spherical regular polygon base bodies are spliced into the sphere through mutual meshing of the first connecting structure and the second connecting structure, and the multiple spherical regular polygon base bodies forming the sphere have the same side edge number or have different side edge numbers. The total number of the first connecting structures and the second connecting structures on the side edges of the multiple spherical regular polygon base bodies forming the sphere is equal, spherical dense laying of a three-dimensional layer can be achieved, and compared with a two-dimensional dense laying system, the spherical dense laying system has a wider application space.

Description

Technical Field

[0001] The invention relates to the technical field of spherical tessellation structures, and in particular to a spherical tessellation system based on regular polygons. Background Art

[0002] Plane tiling refers to a method of laying out a certain area on a plane so that the entire plane is seamlessly covered without leaving blank spaces or overlapping. Plane tiling has aroused people's interest as early as ancient Greece, and its applications cover many fields. In mathematics, plane tiling is widely used to study geometric and topological problems. In the field of art, plane tiling is used to design patterns and decorations, such as the famous Morse pattern, which is a plane tiling structure. In the field of engineering, plane tiling is used to manufacture complex structures and materials, such as architectural design and textile manufacturing. Plane tiling is the most familiar and commonly used type of tiling. Chinese patent CN200610065866.6 discloses a tiling plane system, which considers the splicing of plane systems and cannot be tiled on a three-dimensional level.

[0003] Spherical tessellation is to cover the sphere with a limited number of spherical blocks, but without overlapping or gaps. Spherical tessellation can effectively divide the sphere into small areas, so that each area can be covered without gaps. It is widely used in geography, astronomy, computer graphics and other fields, and is of great significance in making maps, designing celestial models, and creating virtual environments. For example, map projection is an application of spherical tessellation, which realizes the production and use of maps by projecting the earth's surface onto a plane.

[0004] Compared with plane tiling, spherical space tiling is very rare. This is because the mathematical principles and technical implementation of tiling a sphere without gaps or overlaps are much more complicated than those of a plane.

[0005] The spherical tessellation reported so far is relatively limited, and regular polygons are the simplest and most important basic tessellation units. Therefore, how to develop a spherical tessellation system based on regular polygons is an urgent problem to be solved by those skilled in the art. Summary of the invention

[0006] In view of this, the present invention provides a spherical tiling system based on spherical regular polygons, which can achieve spherical tiling on a three-dimensional level and has a wider application space than a two-dimensional tiling system.

[0007] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme: a spherical paving system based on regular polygons, which includes multiple spherical regular polygon matrices, and the spherical regular polygon matrices are all based on spherical regular polygons. Each side of each spherical regular polygon matrix is ​​provided with a first connecting structure or a second connecting structure or a first connecting structure and a second connecting structure. The outer contour shape of the first connecting structure is adapted to the outer contour shape of the second connecting structure. The multiple spherical regular polygon matrices are spliced ​​into a sphere through the mutual engagement of the first connecting structure and the second connecting structure. The multiple spherical regular polygons constituting the sphere have the same number of sides or different numbers of sides, and the total number of the first connecting structures and the second connecting structures on the sides of the multiple spherical regular polygons constituting the sphere is equal.

[0008] The beneficial effects of the present invention are as follows: multiple spherical substrates are spherical regular polygons, wherein multiple spherical regular polygons with the same number of sides can be spliced ​​into a sphere, such as the splicing of multiple spherical regular triangles. In addition, multiple spherical regular polygons with different numbers of sides can also be spliced ​​into a sphere, such as the splicing of an appropriate number of spherical regular triangles and an appropriate number of spherical regular quadrilaterals. In addition, there are at least two specific splicing structure forms, one is the splicing of each side of the substrate with one connection structure, and the other is the splicing of each side of the substrate with multiple connection structures. It should be noted that no matter the splicing of one connection structure or multiple connection structures, it is necessary to ensure that the number of matching substructures of the splicing structure is equal, otherwise it cannot be effectively spliced ​​into a sphere.

[0009] Preferably, when a connecting structure is provided on each side of the multiple spherical regular polygonal bases constituting the sphere, the first connecting structure or the second connecting structure on the side of each spherical regular polygon is located at the center of the side, and the first connecting structure on each side of the spherical regular polygon is adapted to fit and splice with the second connecting structure on the side of the adjacent spherical regular polygon.

[0010] The resulting technical effect is that the connection structure in this solution is located at the center of the side, which actually satisfies the possibility of splicing a variety of spherical substrates. The use of such spherical regular polygonal substrates can be adapted to fit and splice together to form a complete sphere.

[0011] Preferably, when there is only one connecting structure on each side of the multiple spherical regular polygons constituting the sphere, the connecting structure is located at the center of the side, the multiple spherical regular polygons can be the same type of spherical regular polygons with an equal number of sides, or multiple types of spherical regular polygons with different numbers of sides, and the connecting structure is a recess or a protrusion. The multiple spherical regular polygons constituting the sphere respectively have a recess and a protrusion on adjacent sides, and the recesses and protrusions on the adjacent sides of the spherical regular polygons that are spliced ​​together are adapted to fit together.

[0012] The resulting technical effect is: the scheme is discussed on the basis of a connecting structure on the side, and there are two series of combinations in this case. One series is composed of multiple spherical regular polygons with the same number of sides, for example, multiple spherical regular quadrilateral bases; the other series is composed of multiple spherical regular polygons with different numbers of sides, for example, a combination of multiple spherical regular triangles and multiple spherical regular tetrahedrons. It should be noted that all splicing methods in this case need to ensure the matching of the number of recesses and protrusions on the side, otherwise they cannot be effectively engaged.

[0013] Preferably, when a plurality of connection structures are provided on the side of the spherical regular polygon matrix constituting the sphere, the first connection structure and the second connection structure on each side of the spherical regular polygon form 180-degree rotational symmetry about the midpoint of the side, and the spherical matrix forms rotational symmetry about the center of the regular polygon.

[0014] The resulting technical effect is: in this solution, the rotational symmetry of the spherical regular polygon about the center is guaranteed, and such spherical regular polygon matrix can be spliced ​​to form a sphere.

[0015] Preferably, when the sides of the spherical regular polygon constituting the sphere are provided with a plurality of connecting structures, the spherical regular polygon can be the same type of spherical regular polygons with the same number of sides, or multiple types of spherical regular polygons with different numbers of sides, and the first connecting structures are all recesses or protrusions, and the recesses and protrusions on each side form a 180-degree rotational symmetry corresponding to the midpoint of the side.

[0016] The resulting technical effect is: the scheme is a discussion based on the side having multiple connecting structures, and this case also has two series of combinations, one series is the combination of multiple similar spherical regular polygons with equal number of sides, such as the combination of multiple spherical regular quadrilaterals, and the other series is the combination of multiple different types of spherical regular polygons with unequal number of sides, for example, the combination of multiple spherical regular triangles and multiple spherical regular quadrilaterals. In this case, it is necessary to ensure that the multiple connecting structures (notches and protrusions) on the side are rotationally symmetric about the center of the side, and it is also necessary to ensure that the multiple connecting structures on adjacent edges of the spherical regular polygons can fit and engage with each other.

[0017] Preferably, the lengths of the sides of the spherical regular polygons constituting the sphere are equal, whether the number of sides is the same or different.

[0018] The resulting technical effect is that only spherical regular polygons with equal side lengths but different numbers of sides can complete the tiling of the entire sphere.

[0019] Preferably, the spherical regular polygons with the same or different numbers of sides constituting the sphere correspond one-to-one to the number of sides, quantity and arrangement order of the five regular polyhedrons or thirteen Archimedean solids when spliced.

[0020] The resulting technical effect is that the dense tiling of the spherical regular polygonal matrix corresponds to five regular polyhedrons or thirteen Archimedean solids. It can be understood that the five regular polyhedrons (including the regular tetrahedron, the regular hexahedron, the regular octahedron, the regular dodecahedron and the regular icosahedron) or the thirteen Archimedean solids are similarly replaced by spherical polygons, and this logical law is followed to ensure the smooth dense tiling of the sphere. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a schematic diagram of Example 1 of a spherical tessellation system based on regular polygons of the present invention;

[0022] Figure 2 It is a schematic diagram of Example 2 of a spherical tessellation system based on regular polygons of the present invention;

[0023] Figure 3 It is a schematic diagram of Example 3 of a spherical tessellation system based on regular polygons of the present invention;

[0024] Figure 4 It is a schematic diagram of Example 4 of a spherical tessellation system based on regular polygons of the present invention;

[0025] Figure 5 It is a schematic diagram of Example 5 of a spherical tessellation system based on regular polygons of the present invention;

[0026] Figure 6 It is a schematic diagram of Example 6 of a spherical tessellation system based on regular polygons of the present invention;

[0027] Figure 7 It is a schematic diagram of Example 7 of a spherical tessellation system based on regular polygons of the present invention;

[0028] Figure 8 It is a schematic diagram of Example 8 of a spherical tessellation system based on regular polygons of the present invention;

[0029] Fig. 9 It is a schematic diagram of Example 9 of a spherical tessellation system based on regular polygons of the present invention;

[0030] Fig.10 It is a schematic diagram of Example 10 of a spherical tessellation system based on regular polygons of the present invention;

[0031] Fig.11 It is a schematic diagram of Example 11 of a spherical tessellation system based on regular polygons of the present invention;

[0032] Fig.12 It is a schematic diagram of Example 12 of a spherical tessellation system based on regular polygons of the present invention;

[0033] Fig.13 It is a schematic diagram of Example 13 of a spherical tessellation system based on regular polygons of the present invention;

[0034] Fig.14 It is a schematic diagram of Example 14 of a spherical tessellation system based on regular polygons of the present invention;

[0035] Fig.15 It is a schematic diagram of Example 15 of a spherical tessellation system based on regular polygons of the present invention;

[0036] Fig.16 It is a schematic diagram of Example 16 of a spherical tessellation system based on regular polygons of the present invention;

[0037] Fig.17 It is a schematic diagram of Example 17 of a spherical tessellation system based on regular polygons of the present invention;

[0038] Fig.18 It is a schematic diagram of Example 18 of a spherical tessellation system based on regular polygons of the present invention;

[0039] Fig.19 It is a schematic diagram of Example 19 of a spherical tessellation system based on regular polygons of the present invention;

[0040] Fig. 20 It is a schematic diagram of Example 20 of a spherical tessellation system based on regular polygons of the present invention;

[0041] Fig.21 It is a schematic diagram of Example 21 of a spherical tessellation system based on regular polygons of the present invention;

[0042] Fig. 22 It is a schematic diagram of Example 22 of a spherical tessellation system based on regular polygons of the present invention;

[0043] Fig.23 It is a schematic diagram of Example 23 of a spherical tessellation system based on regular polygons of the present invention;

[0044] Fig.24 It is a schematic diagram of Example 24 of a spherical tessellation system based on regular polygons of the present invention;

[0045] Fig.25 It is a schematic diagram of Example 25 of a spherical tessellation system based on regular polygons of the present invention;

[0046] Fig.26 It is a schematic diagram of Example 26 of a spherical tessellation system based on regular polygons of the present invention;

[0047] Fig. 27 It is a schematic diagram of Example 27 of a spherical tessellation system based on regular polygons of the present invention;

[0048] Fig.28 It is a schematic diagram of Example 28 of a spherical tessellation system based on regular polygons of the present invention;

[0049] Fig.29 It is a schematic diagram of Example 29 of a spherical tessellation system based on regular polygons of the present invention;

[0050] Fig.30 It is a schematic diagram of Example 30 of a spherical tessellation system based on regular polygons of the present invention;

[0051] Fig.31 It is a schematic diagram of Example 31 of a spherical tessellation system based on regular polygons of the present invention;

[0052] Fig.32 It is a schematic diagram of Example 32 of a spherical tessellation system based on regular polygons of the present invention;

[0053] Fig.33 It is a schematic diagram of Example 33 of a spherical tessellation system based on regular polygons of the present invention;

[0054] Fig.34 It is a schematic diagram of Example 34 of a spherical tessellation system based on regular polygons of the present invention;

[0055] Fig.35 It is a schematic diagram of Example 35 of a spherical tessellation system based on regular polygons of the present invention;

[0056] Fig.36 It is a schematic diagram of Example 36 of a spherical tessellation system based on regular polygons of the present invention;

[0057] Fig.37 This is a schematic diagram of Example 37 of a spherical tiling system based on regular polygons of the present invention.

[0058] 1 spherical regular polygon, 2 concave, 3 convex. 4 side. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] See the attached Figures 1 to 37According to an embodiment of the present invention, a spherical tiling system based on regular polygons includes a plurality of spherical regular polygonal bases, and the plurality of spherical regular polygonal bases are spliced ​​together to form a sphere. The spherical regular polygonal bases are all based on a spherical regular polygon 1. The plurality of spherical regular polygons 1 constituting the sphere have the same number of sides or have different numbers of sides. It can be understood that the sphere can be composed of a single splicing of a plurality of spherical regular triangles or spherical regular quadrilaterals or other spherical regular polygons, or can be composed of a combination of a plurality of spherical regular polygons with different numbers of sides. The present invention can be specifically divided into two large series of combinations. One series of combinations is a splicing state in which a plurality of connection structures are present on the sides of a spherical regular polygon. See attached Figure 1-18 Another series of combinations is the state where there is only one connection structure on the side of the spherical regular polygon. Figure 19-37 .

[0061] Specifically, there is one connection structure (the first connection structure or the second connection structure) on one side of the spherical regular polygon 1, or there are two connection structures (the first connection structure and the second connection structure) at the same time. It should be noted that the outer contours of the first connection structure and the second connection structure can be interlocked and spliced. When there is one connection structure spliced ​​on one side, the connection structure needs to be arranged at the center of the side. In addition, the total number of the first connection structure and the second connection structure on the side of the spherical regular polygon substrate needs to be equal.

[0062] When there are two connecting structures on a side, that is, the first connecting structure and the second connecting structure are provided on the side of the spherical regular polygon base constituting the sphere, in this case, the first connecting structure and the second connecting structure on the side form a 180-degree rotational symmetry about the midpoint of the side. In addition, the spherical regular polygon forms rotational symmetry about the center, which ensures the universality of each spherical regular polygon and facilitates mutual fit.

[0063] Specifically, when the spherical regular polygonal bases constituting the sphere have the same number of sides, for example, when the batch of spherical regular polygonal bases are all spherical regular triangles, the same side of the corresponding spherical regular triangles are provided with recesses 2 and protrusions 3 for engaging with adjacent spherical regular triangles, and the recesses 2 and protrusions 3 on the adjacent spherical regular triangles constituting the sphere engage with each other.

[0064] More specifically, when the spherical regular polygonal bases constituting the sphere have different numbers of sides, for example, the batch of spherical regular polygonal bases are spherical regular triangles and spherical regular quadrilaterals, then only the notch 2 is provided on multiple sides of the spherical regular triangle, or only the convex block 3 is provided, or both the notch 2 and the convex block 3 are provided on the same side, or the notch 2 and the convex block 3 are provided on adjacent sides respectively, and only the notch 2 is provided on multiple sides of the spherical regular quadrilateral, or only the convex block is provided 3, or both the notch 2 and the convex block 3 are provided on the same side, or the notch 2 and the convex block 3 are provided on adjacent sides respectively, and when matched, it is the bite of the notch and the convex block, then the convex block or the notch cannot be provided on the side of the spherical regular polygon substrate at the same time, specifically, the notch on the spherical regular triangle and the convex block on the spherical regular quadrilateral are adapted to bite and splice, or the spherical regular triangle with specific notches and convex blocks and the spherical regular quadrilateral with notches and convex blocks are adapted to bite and splice.

[0065] It should be noted that the splicing of spherical regular polygons is not limited to the method of notches and protrusions, and other connection methods are also possible.

[0066] Specifically, when a side has both a notch and a protrusion, the notch and the protrusion form rotational symmetry of 180 degrees about the midpoint of the side of the spherical regular polygon substrate, thereby improving the versatility of the tile substrate and facilitating the snap connection of spherical regular polygons with different numbers of sides.

[0067] In addition, the side lengths of the spherical regular polygonal matrices that constitute the sphere must be equal, which is the basis for ensuring that the spherical regular polygonal matrices can be smoothly spliced ​​into a sphere.

[0068] The splicing method and process refer to the five regular polyhedrons or thirteen Archimedean solids. The spherical regular polygonal matrix that constitutes the sphere corresponds one by one to the number of sides, quantity and arrangement order of the five regular polyhedrons or the thirteen Archimedean solids when splicing. It can be understood that the multiple planar polygons of the five regular polyhedrons (regular tetrahedron, regular hexahedron, regular octahedron, regular dodecahedron, regular icosahedron) or thirteen Archimedean solids can be replaced with spherical regular polygons for snap-fitting and connection.

[0069] It should be noted that the embodiments of the present invention are that the categories of the multiple spherical regular polygonal bases that constitute the sphere are of the same type, that is, the midpoints of the sides of all the spherical regular polygonal bases are either provided with a notch or a protrusion, or the sides of all the spherical regular polygonal bases have a pair of notches and protrusions with 180-degree rotational symmetry about the midpoint of the side.

[0070] Reference Figure 1 , this embodiment 1 is a schematic diagram of a spherical splicing structure of multiple (333) spherical regular triangles, and there are recesses and convex structures on the same side of the spherical regular triangles; 333 means that three spherical regular triangles are combined at one vertex.

[0071] Reference Figure 2 , this embodiment 2 is a schematic diagram of a spherical splicing structure of multiple (444) spherical regular quadrilaterals, and there are notches and convex block structures on the same side of the spherical regular quadrilateral;

[0072] Reference Figure 3 , this embodiment 3 is a schematic diagram of sphere splicing of multiple (3333) spherical regular triangles, and the difference from embodiment 1 is that the number of spherical regular triangles is increased;

[0073] Reference Figure 4 , this embodiment 4 is a schematic diagram of a sphere splicing a plurality of (555) spherical regular pentagons, and there are notches and convex block structures on the same side of the spherical regular pentagons;

[0074] Reference Figure 5 , this embodiment 5 is a schematic diagram of a sphere splicing structure of multiple (33333) spherical regular triangles, and the number of spherical regular triangles is increased compared to embodiment 3;

[0075] Reference Figure 6 , this embodiment 6 is a schematic diagram of a spherical splicing structure composed of a plurality of (3434) spherical regular triangles and spherical regular quadrilaterals, and there are notches and convex block structures on the same side of the spherical regular triangles and the spherical regular quadrilaterals;

[0076] Reference Figure 7 , this embodiment 7 is a schematic diagram of a spherical structure composed of multiple (3535) spherical regular triangles and spherical regular pentagons, and there are concave and convex structures on the same side of the spherical regular triangle and the spherical regular pentagon;

[0077] Reference Figure 8 , this embodiment 8 is a schematic diagram of a spherical structure composed of a plurality of (366) spherical regular triangles and spherical regular hexagons, wherein the spherical regular triangles and the spherical regular hexagons have a concave and convex structure on the same side;

[0078] Reference Fig. 9 , this embodiment 9 is a schematic diagram of a spherical structure composed of multiple (388) spherical regular triangles and spherical regular octagons, and there are notches and convex block structures on the same side of the spherical regular triangles and the spherical regular octagons;

[0079] Reference Fig.10 , this embodiment 10 is a schematic diagram of a spherical structure composed of a plurality of (466) spherical regular quadrilaterals and spherical regular hexagons, wherein the spherical regular quadrilaterals and the spherical regular hexagons have a concave and convex structure on the same side;

[0080] Reference Fig.11, this embodiment 11 is a schematic diagram of a spherical structure composed of multiple (3444) spherical regular triangles and spherical regular quadrilaterals, and there are notches and convex block structures on the same side of the spherical regular triangle and the spherical regular quadrilateral;

[0081] Reference Fig.12 , this embodiment 12 is a schematic diagram of a spherical structure composed of a plurality of (468) spherical regular quadrilaterals, spherical regular hexagons and spherical regular octagons, wherein the spherical regular quadrilaterals, spherical regular hexagons and spherical regular octagons have concave and convex structures on the same side;

[0082] Reference Fig.13 , Example 13 is a schematic diagram of a spherical structure of a combination of multiple (33334) spherical regular triangles and spherical regular quadrilaterals. The spherical regular quadrilaterals and spherical regular triangles have concave and convex structures on the same side, which is a different splicing combination from Examples 6 and 11;

[0083] Reference Fig.14 , this embodiment 14 is a schematic diagram of a spherical structure composed of a plurality of (566) spherical regular pentagons and spherical regular hexagons, wherein the same side of the spherical regular pentagons and the spherical regular hexagons has a concave and convex structure;

[0084] Reference Fig.15 , this embodiment 15 is a schematic diagram of a spherical structure composed of a plurality of (3454) spherical regular triangles, spherical regular quadrilaterals and spherical regular pentagons, wherein the same side of the spherical regular triangles, spherical regular quadrilaterals and spherical regular pentagons has a concave and convex structure;

[0085] Reference Fig.16 , this embodiment 16 is a schematic diagram of a spherical structure composed of multiple (33335) spherical regular triangles and spherical regular pentagons, and there are recesses and convex block structures on the same side of the spherical regular triangles and the spherical regular pentagons;

[0086] Reference Fig.17 , this embodiment 17 is a schematic diagram of a spherical structure composed of a plurality of (4610) spherical regular quadrilaterals, spherical regular hexagons and spherical regular decagons, wherein the spherical regular quadrilaterals, spherical regular hexagons and spherical regular decagons have concave and convex structures on the same side;

[0087] Reference Fig.18 , this embodiment 18 is a schematic diagram of a spherical structure composed of multiple (31010) spherical regular triangles and spherical regular decagons, and there are notches and convex block structures on the same side of the spherical regular triangles and the spherical regular decagons;

[0088] Embodiment 1-18 is a schematic diagram of a combination in which a side has two connection structures (a notch and a protrusion).

[0089] Attached Figure 19-37 This is a schematic diagram of a combination when a side has only one connection structure. It should be noted that the connection structure is located at the center of the side, and at the same time, the number of recesses and the number of protrusions on the sides of multiple spherical regular polygons must be equal.

[0090] Reference Fig.19 , this embodiment 19 is a schematic diagram of a spherical structure of a plurality of (444) spherical regular quadrilaterals spliced ​​together, and there are notches and convex block structures on the adjacent sides of the spherical regular quadrilaterals, that is, there is only one connecting structure on one side;

[0091] Reference Fig. 20 , this embodiment 20 is a schematic diagram of a spherical structure composed of a plurality of (466) spherical regular quadrilaterals and spherical regular hexagons, wherein adjacent sides of the spherical regular quadrilaterals and spherical regular hexagons have recesses and convex block structures;

[0092] Reference Fig.21 , this embodiment 21 is a schematic diagram of a spherical structure composed of a plurality of (468) spherical regular quadrilaterals, spherical regular hexagons and spherical regular octagons, wherein adjacent sides of the spherical regular quadrilaterals, spherical regular hexagons and spherical regular octagons have concave and convex structures;

[0093] Reference Fig. 22 , this embodiment 22 is a schematic diagram of a spherical structure composed of a plurality of (4610) spherical regular quadrilaterals, spherical regular hexagons and spherical regular decagons, wherein adjacent sides of the spherical regular quadrilaterals, spherical regular hexagons and spherical regular decagons have concave and convex structures;

[0094] Reference Fig.23 , this embodiment 23 is a schematic diagram of a spherical structure composed of a plurality of (388) spherical regular triangles and spherical regular octagons, the sides of the spherical regular triangles are all convex structures, and the adjacent sides of the spherical regular octagons have concave and convex structures;

[0095] Reference Fig.24 , this embodiment 24 is a schematic diagram of a spherical structure composed of a plurality of (3454) spherical regular triangles, spherical regular quadrilaterals and spherical regular pentagons, wherein the spherical regular triangles and spherical regular pentagons have convex block structures on their sides, and the spherical regular quadrilaterals have concave structures on their sides;

[0096] Reference Fig.25 , this embodiment 25 is a schematic diagram of a spherical structure composed of a plurality of (3434) spherical regular triangles and spherical regular quadrilaterals, wherein the sides of the spherical regular triangles are all convex structures, and the sides of the spherical regular quadrilaterals are all concave structures;

[0097] Reference Fig.26, this embodiment 26 is a schematic diagram of a spherical structure composed of a plurality of (3535) spherical regular triangles and spherical regular pentagons, wherein the sides of the spherical regular triangles are all convex structures, and the sides of the spherical regular pentagons are all concave structures;

[0098] Reference Fig. 27 , this embodiment 27 is a schematic diagram of a spherical structure composed of multiple (566) spherical regular pentagons and spherical regular hexagons. The side of the spherical regular pentagon has a connecting structure, which can be a convex structure or a concave structure. The side of the spherical regular hexagon also has a connecting structure, which can be a convex structure or a concave structure. Of course, there are no excessive restrictions on whether the structures on each side of the same spherical regular polygon are the same.

[0099] Reference Fig.28 , Example 28 is also a schematic diagram of a spherical structure composed of a plurality of (566) spherical regular pentagons and spherical regular hexagons. Compared with Example 27, the layout of the connection structure on the side of the spherical regular polygon is different.

[0100] Reference Fig.29 , Example 29 is a schematic diagram of a spherical structure composed of multiple (33334) spherical regular triangles and spherical regular quadrilaterals. The side of the spherical regular triangle or the spherical regular quadrilateral has a connecting structure, which can be a protrusion structure or a recessed structure. Compared with Example 13, the layout of the spliced ​​connecting structure is different.

[0101] Reference Fig.30 , this embodiment 30 is a schematic diagram of the splicing of multiple (3333) spherical regular triangles, and there is a recess or a protrusion on the adjacent sides.

[0102] Reference Fig.31 , this embodiment 31 is a schematic diagram of the splicing of multiple (555) spherical regular pentagons. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular pentagons needs to be equal.

[0103] Reference Fig.32 This embodiment 32 is a schematic diagram of the splicing of multiple (33333) spherical regular triangles. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles needs to be equal.

[0104] Reference Fig.33, this embodiment 33 is a schematic diagram of the splicing of multiple (366) spherical regular triangles and spherical regular hexagons. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles and spherical regular hexagons must be equal.

[0105] Reference Fig.34 , this embodiment 34 is a schematic diagram of the spherical splicing of multiple (3444) spherical regular triangles and spherical regular quadrilaterals. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles and spherical regular quadrilaterals must be equal.

[0106] Reference Fig.35 , Example 35 is a schematic diagram of the splicing of multiple (33334) spherical regular triangles and spherical regular quadrilaterals. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles and spherical regular quadrilaterals needs to be equal.

[0107] Reference Fig.36 , this embodiment 36 is a schematic diagram of the splicing of multiple (31010) spherical regular triangles and spherical regular decagons. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles and spherical regular decagons needs to be equal.

[0108] Reference Fig.37 , Example 37 is a schematic diagram of the splicing of multiple (33335) spherical regular triangles and spherical regular pentagons. It is necessary to ensure that there is a recess or a protrusion on the adjacent sides, that is, the total number of recesses and protrusions on the sides of all spherical regular triangles and spherical regular pentagons must be equal.

[0109] Examples 19-37 are actually schematic diagrams of a combination in which there is only one connection structure on the side of the base, that is, a schematic diagram of a combination in which one side has a recess or a protrusion.

[0110] It should be noted that the first connection structure and the second connection structure are not limited to the notch and the protrusion, and may also be other structures that can be engaged.

[0111] In summary of all the above embodiments, it should be noted that, under the corresponding relationship of the central projection, the number of sides, quantity and arrangement order of the spherical regular polygonal matrix on each spherical tiling correspond one-to-one to the regular polyhedron (5 types) or Archimedean body (13 types), respectively. Therefore, the sides (minor arcs of the great circle) of all spherical regular polygonal matrixes are of equal length; each side of the spherical regular polygonal matrix is ​​designed with a set of protrusions and recesses, and the protrusions and recesses of all sides are the same in shape and size, and this set of buckles forms a 180° rotational symmetry about the midpoint of the edge, and the edges of the spherical regular polygonal matrix designed with buckles form central rotational symmetry about the center of the regular polygonal matrix.

[0112] Under the corresponding relationship of the central projection, the number of sides, quantity and arrangement order of the spherical regular polygonal matrix on each spherical tessellation correspond to the regular polyhedron (5 types) or Archimedean solid (13 types) respectively; therefore, the sides (minor arcs of the great circle) of all spherical regular polygonal matrixes are of equal length; the midpoint of each side of the spherical regular polygonal matrix is ​​designed with protruding or recessed buckles, and the size and shape of the buckles are the same; the number of protruding buckles and recessed buckles of all regular polygonal matrices in each spherical tessellation is equal, and under the corresponding relationship of the central projection, the regular polygons of the aforementioned regular polyhedron (5 types) or Archimedean solid (13 types) are replaced by the aforementioned spherical regular polygonal matrix to complete the splicing combination of the sphere.

[0113] As for the device and the method of use disclosed in the embodiment, since they correspond to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0114] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A spherical tessellation system based on regular polygons, characterized in that: It includes multiple spherical regular polygonal bases, all of which are based on spherical regular polygons. A first connecting structure or a second connecting structure or a first connecting structure and a second connecting structure are provided on each side of each spherical regular polygonal base. The outer contour shape of the first connecting structure is adapted to the outer contour shape of the second connecting structure. The multiple spherical regular polygonal bases are spliced ​​into a sphere through the mutual engagement of the first connecting structure and the second connecting structure. The multiple spherical regular polygonal bases constituting the sphere have the same number of sides or different numbers of sides, and the total number of the first connecting structures and the second connecting structures on the sides of the spherical regular polygonal bases constituting the sphere is equal.

2. A spherical tessellation system based on regular polygons according to claim 1, characterized in that: When a connecting structure is provided on each side of the multiple spherical regular polygonal bases constituting the sphere, the first connecting structure or the second connecting structure on the side of each spherical regular polygonal base is located at the center of the side, and the first connecting structure on the side of each spherical regular polygonal base is adapted to be snap-fitted and spliced ​​with the second connecting structure on the side of the adjacent spherical regular polygonal base, or the second connecting structure on the side of each spherical regular polygonal base is adapted to be snap-fitted and spliced ​​with the first connecting structure on the side of the adjacent spherical regular polygonal base.

3. A spherical tessellation system based on regular polygons according to claim 2, characterized in that: When there is only one connecting structure on each side of the multiple spherical regular polygonal bases constituting the sphere, the connecting structure is located at the center of the side, the multiple spherical regular polygonal bases can have the same number of sides, or have different numbers of sides, the connecting structure is a recess or a protrusion, and the multiple spherical regular polygonal bases constituting the sphere have a recess and a protrusion on adjacent sides respectively, and the multiple spherical regular polygonal bases are adapted to be snap-fitted and spliced ​​through the recesses and protrusions on the adjacent sides.

4. A spherical tessellation system based on regular polygons according to claim 1, characterized in that: When multiple connecting structures are provided on each side of the multiple spherical regular polygonal bases constituting the sphere, the first connecting structure and the second connecting structure on the side of the spherical regular polygonal base form 180-degree rotational symmetry about the midpoint of the side, and the side of the spherical regular polygonal base forms rotational symmetry about the center of the base.

5. A spherical tessellation system based on regular polygons according to claim 4, characterized in that: When multiple connecting structures are provided on each side of multiple spherical regular polygonal bases constituting a sphere, the multiple spherical regular polygonal bases may have the same number of sides or different numbers of sides, and the first connecting structures are all recesses or protrusions, and the recesses and protrusions on each side form 180-degree rotational symmetry about the midpoint of the side.

6. A spherical tessellation system based on regular polygons according to claim 1, characterized in that: The sides of the spherical regular polygons that make up the sphere are of equal length.

7. A spherical tessellation system based on regular polygons according to any one of claims 1 to 6, characterized in that: The spherical regular polygonal bases constituting the sphere correspond one to one with the number of sides, quantity and arrangement order of the five regular polyhedrons or thirteen Archimedean solids when spliced.

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