Spherical tiling puzzle

Abstract

We provide a spherical tiling puzzle formed by combining multiple spherical pieces. [Solution] The spherical pieces of the present invention are set up using spherical regular polygons as the basic design element, and the multiple spherical regular polygon pieces constituting the spherical puzzle have the same or different number of sides, and the multiple spherical regular polygon pieces can be joined to a hollow spherical puzzle according to the surface layout of five types of regular polyhedra or thirteen types of Archimedean bodies, and the spherical pieces set up by deforming spherical regular polygons as the basic design element have multiple types of outer contour shapes, including but not limited to polygonal, animal-like, and human figure-like shapes, and the present invention can realize spherical filling of three-dimensional solid structures, and the filling method is diverse and has a wider range of applications.

Description

Technical Field

[0001] The present invention relates to the technical field of spherical filling structures, and specifically to a method for the spherical filling structure of hollow spherical puzzles.

Background Art

[0002] Plane tiling refers to a sealing method that covers the entire plane without gaps by covering a certain area on the plane, without any white space or overlap. Plane tiling has attracted people's attention since ancient Greece, and its applications cover many fields. Mathematically, plane tiling is widely applied to the study of geometric and topological problems. In the art field, plane tiling is used for design patterns and decorations. For example, the famous moiré pattern is a plane tiling structure. In the construction field, plane tiling is used for the manufacture of complex structures and materials such as building design and fabric manufacturing. Plane tiling is the most well-known and commonly used filling type among people. However, conventional patents (such as the filling plane system of Chinese Patent CN200610065866.6) mainly focus on the joining of plane systems and cannot realize a filling structure at the three-dimensional level.

[0003] Spherical filling covers the sphere with a single connected spherical block without allowing overlap or gaps. Spherical filling can effectively divide the sphere into small areas, thereby covering each area without gaps, and is widely applied in fields such as geography, celestial bodies, and computer graphics. For example, map projection is an application of spherical filling, which realizes the creation and use of maps by projecting the surface of the earth onto a plane. Compared with plane tiling, the filling of spherical space is very rare because the realization of the technology for filling the sphere without gaps and without overlap is much more complex than that of the plane. The currently reported spherical fillings are relatively limited, and regular polygons are the simplest and most important filling elements.

[0004] Conventional spherical puzzle patents (e.g., Japanese patents JP2006334192A, JP2006334263A, and JP3166704U) have increased the interest and complexity of the puzzles to some extent, but their structure is relatively simple and their potential for development is limited. These patents mainly focus on realizing spherical puzzles by combining and joining multiple types of regular polygons, and lack innovation and diversity.

[0005] Current spherical puzzles primarily appear in the toy and education markets (e.g., Earth sphere puzzles), and their content and depth are limited, resulting in low added value. Furthermore, the relatively simple structural technology of conventional spherical puzzles leads to a lack of patent barriers and technological innovation, resulting in severe product competition.

[0006] Therefore, how to construct new spherical puzzles to provide more flexible construction methods, a wider range of application environments, richer external structures, and more objective economic potential, thereby ensuring that spherical puzzles possess more outstanding characteristics and competitiveness in economic, scientific puzzle, knowledge education, and art aspects, and demonstrating broader future application potential, is a problem that those skilled in the art should urgently address. [Overview of the project]

[0007] In view of this, the present invention provides a spherical tiling puzzle that can realize spherical tiling at the three-dimensional level, has diverse puzzle structure forms, and has a wider range of applications.

[0008] To achieve the above objectives, the present invention employs the following technical solution: A spherical tiling puzzle comprising a plurality of spherical pieces, wherein the spherical pieces are set up using spherical regular polygons as basic design elements, the spherical regular polygon pieces constituting the spherical puzzle have the same or different numbers of sides, the plurality of spherical regular polygon pieces can be joined to a hollow sphere according to the surface layout of five types of regular polyhedra or thirteen types of Archimedean bodies, and the spherical pieces set up by deforming spherical regular polygons as basic design elements have multiple types of outer contour shapes, including but not limited to polygonal, animal-like, and human figure-like shapes.

[0009] The beneficial effects of the present invention are as follows: The spherical pieces of the spherical tiling puzzle include two series. The outer contour shape of the first series is spherical polygonal, and the outer contour shape of the second series is animal-shaped and human-shaped spherical pieces. A common feature of these series is that all spherical pieces use a regular spherical polygon as their basic design element. The polygonal pieces are structurally designed on their sides based on a regular polygon, while the animal-shaped and human-shaped pieces are designed on a regular polygon as their design basis, with corresponding deformation curves applied to them.

[0010] Preferably, when the outer contour shape of the pieces constituting the spherical puzzle is a spherical regular polygon, a first connecting structure or a second connecting structure is provided on the side of the spherical regular polygon piece, or both the first and second connecting structures are provided simultaneously, the outer contour shapes and sizes of the provided first and second connecting structures are the same, the multiple spherical regular polygon pieces are joined to the sphere by interlocking along the sides of the first and second connecting structures, the total number of first and second connecting structures provided on the spherical regular polygon pieces in the joined sphere is equal, and the lengths of the side edges of the spherical regular polygon pieces constituting the spherical puzzle are the same.

[0011] The technical effects of this are as follows: A spherical puzzle is formed by joining multiple spherical regular polygon pieces, and these spherical regular polygon pieces can have the same or different numbers of sides. The lengths of the sides of all spherical regular polygon pieces are equal, which ensures that the first and second connecting structures on the sides are precisely aligned, fit together, and interlock to join the sphere. The total number of first connecting structures on the sides of the spherical regular polygon pieces in the joined sphere is equal to the total number of second connecting structures, which ensures that the first and second connecting structures can pair and interlock to form a stable spherical puzzle.

[0012] When the outer contour shape of a spherical piece is similar to multiple types of regular spherical polygons, there are two design approaches for the connection structure of the sides of the regular spherical polygon piece. The first approach is for the sides of the regular spherical polygon piece to have multiple connection structures, and the second approach is for the sides of the regular spherical polygon piece to have only one type of connection structure.

[0013] Preferably, when multiple connecting structures are provided on the sides of regular polygonal pieces constituting a spherical puzzle, the lengths of the sides of the spherical regular polygonal pieces are the same, the shapes and sizes of the first and second connecting structures on the sides of the pieces are the same, and the connecting structures form 180 degrees of rotational symmetry with respect to the midpoint of the side, and the sides of the spherical pieces on which the connecting structures are provided form rotational symmetry with respect to the center of the spherical piece.

[0014] As a result of this, the solution represents the first situation of the first series, in which the lengths of the sides of the spherical regular polygon pieces coincide, and the first and second connecting structures on the sides of the pieces form 180-degree rotational symmetry with respect to the midpoint of the sides. When the sides of two pieces are aligned, the first and second connecting structures of the spherical pieces fit and interlock precisely with each other. This allows the pieces to interlock and join precisely, regardless of whether the spherical regular polygon pieces are the same or not, providing extremely great convenience and flexibility.

[0015] Preferably, when only one connecting structure is provided on the side of each regular polygon piece constituting the spherical puzzle, the lengths of the side edges of the spherical regular polygon pieces coincide, the first or second connecting structure on the side edge of the piece is provided at the midpoint of the side edge, multiple types of spherical regular polygon pieces fit together by aligning their side edges, and the first and second connecting structures on the side edges of adjacent spherical regular polygon pieces fit together and join.

[0016] The technical effects of this are as follows: This solution is the second configuration of the first series, in which the connecting structure is located at the midpoint of the side edge of the spherical regular polygon piece, and since the lengths of the side edges match, when aligning the side edges of two pieces, the first connecting structure on the spherical piece and the second connecting structure on the side edge of the adjacent spherical piece fit and interlock precisely. This allows spherical regular polygon pieces with the same number of side edges or different number of side edges to interlock and join, providing extremely great convenience and flexibility.

[0017] In the two above-mentioned approaches, the first type involves providing first and second connecting structures on the sides of the spherical regular polygon pieces, having 180 degrees of rotational symmetry with respect to the midpoint of the side; the second type involves providing only one first or second connecting structure at the midpoint of the side of the spherical regular polygon piece. Pieces with such connecting structures on their sides can be joined to the corresponding spherical puzzle if the types, quantities, and combination methods of the spherical regular polygon pieces correspond one-to-one with the types, quantities, and combination methods of the five regular polyhedra or the thirteen Archimedean regular polygons.

[0018] Preferably, based on the symmetric geometric structure of a regular polyhedron and an Archimedean field, a specific set of curves is designed on the regular polygonal surface of the polyhedron to fit the symmetric features of the polyhedron, based on the contour shape features of an animal or human figure, the designed set of curves is coherently connected on the surface of the polyhedron to form a set of interconnected curves, the set of interconnected curves forming a rotational or mirror symmetry of a specific angle with respect to an axis passing through the midpoint and vertices of the polyhedron, or an axis passing through the midpoint of the polyhedron and the center of a regular polygon, or an axis passing through the midpoint of the polyhedron and the midpoint of a side edge of a regular polygon, or a plane passing through the midpoint of the polyhedron and the edge of a regular polygon, the set of interconnected curves is projected through the center of a sphere, and the sphere is divided into a set of congruent spherical pieces, the outer contours of the set of spherical pieces having contour shape features of an animal or human figure.

[0019] The resulting technical effect is that the above scheme solves the problem of the second series of spherical puzzles, and the pieces constituting the spherical puzzle have identifiable human or animal outer contour features (e.g., outer contour shapes of cats, dogs, flowers, people, etc.). The spherical pieces that make up the puzzle not only have human or animal features but also satisfy the symmetrical structure of a regular polyhedron or Archimedean body. Such spherical pieces can be flexibly changed, closely connected to nature and people's lives, and become puzzles rich in artistic and aesthetic features.

[0020] Preferably, the spherical puzzle is a spherical dog puzzle, the puzzle is designed based on the surface structure features of a cuboctahedron, the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first and second sets of curves are tangent to the polygonal surfaces of the cuboctahedron. Subsequently, 24 sets of interconnected curves are formed, and these interconnected curves have rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to the axis passing through the center and vertices of the cuboctahedron, the axis passing through the center of the cuboctahedron and the center of the square, and the axis passing through the center of the cuboctahedron and the center of the equilateral triangle, respectively. The 24 sets of interconnected curves are projected through the center of the sphere, dividing the sphere into 24 congruent spherical pieces, and the outer contours of these spherical pieces have the external features of a dog.

[0021] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external characteristics of a dog.

[0022] Preferably, the spherical puzzle is a spherical puzzle of a dancing man, the puzzle is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves, the provided set of curves, after being rotated by an integer multiple of 72 degrees around the center of the regular pentagon, form 12 sets of connecting curves that connect the surfaces of the regular dodecahedron, the connecting curves, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a dancing man, and the spherical puzzle joined by the 12 dancing man pieces has 120 degrees of rotational symmetry with respect to the hands and feet of the dancing man.

[0023] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 12 congruent pieces that have the external features of a dancing man.

[0024] Preferably, the spherical puzzle is a spherical puzzle of a person riding a donkey, the puzzle is designed based on the surface structure features of a regular octahedron, the four non-adjacent equilateral triangular faces of the regular octahedron are provided with a first set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, the other four non-adjacent equilateral triangular faces of the regular octahedron are provided with a second set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, the first set of similar curves and the second set of similar curves are connected on the surface of the regular octahedron to form 12 sets of connecting curves, the 12 sets of connecting curves have 180 degrees of rotational symmetry and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular octahedron, and an axis passing through the center and centers of the equilateral triangles, respectively, the 12 sets of connecting curves are projected through the center of the sphere and divide the sphere into 12 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a person riding a donkey.

[0025] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 12 congruent pieces that have the external features of a person riding a donkey.

[0026] Preferably, the spherical puzzle is a butterfly spherical puzzle. The puzzle is designed based on the surface structure characteristics of a cube. On the square faces of the cube, a set of curves having 90-degree rotational symmetry about the center of the face is provided. The set of curves is connected end to end on the polygonal surface of the cube to form 24 sets of connected curves. Each of the 24 sets of connected curves has 120-degree rotational symmetry, 90-degree rotational symmetry, and 180-degree rotational symmetry about the axis passing through the center and vertices of the cube, the axis passing through the center of the cube and the center of the quadrilateral, and the axis passing through the center of the cube and the midpoint of the side of the quadrilateral. After being projected through the center of the sphere, the 24 sets of connected curves divide the sphere into 24 congruent spherical pieces, and the outer contour of the spherical pieces has the external shape characteristics of a butterfly.

[0027] The technical effects thereof are as follows. The spherical puzzle can be formed by joining 24 congruent pieces having the external shape characteristics of a butterfly.

[0028] Preferably, the spherical puzzle is a rabbit spherical puzzle. The puzzle is designed based on the surface structure characteristics of an octahedron. On four non-adjacent equilateral triangle faces of the octahedron, a first set of quasi-curves having 120-degree rotational symmetry about the center of the face is provided. On the other four non-adjacent equilateral triangle faces of the octahedron, a second set of quasi-curves having 120-degree rotational symmetry about the center of the face is provided. The first set of quasi-curves and the second set of quasi-curves are connected end to end on the polygonal surface of the octahedron to form 12 sets of connected curves. Each of the 12 sets of connected curves has 180-degree rotational symmetry, 120-degree rotational symmetry, and mirror symmetry about the axis passing through the center and vertices of the octahedron, the axis passing through the center of the octahedron and the center of the equilateral triangle, and the plane passing through the center of the octahedron and the side of the equilateral triangle. After being projected through the center of the sphere, the 12 sets of connected curves divide the sphere into 12 congruent spherical pieces, and the outer contour of the spherical pieces has the external shape characteristics of a rabbit.

[0029] The technical effects thereof are as follows. The spherical puzzle can be formed by joining 12 congruent pieces having the external shape characteristics of a rabbit.

[0030] Preferably, the spherical puzzle is an octopus spherical puzzle. The puzzle is designed based on the surface structure characteristics of a cuboctahedron. On the square faces of the cuboctahedron, a first set of curves having rotational symmetry of 90 degrees with respect to the center of the face is provided. On the equilateral triangle faces of the cuboctahedron, a second set of curves having rotational symmetry of 120 degrees with respect to the center of the face is provided. The first set of curves and the second set of curves are connected end to end on the polygonal surface of the cuboctahedron to form six sets of connecting curves. The connecting curves have rotational symmetry of 180 degrees, 90 degrees, and 120 degrees respectively with respect to the axis passing through the center and vertices of the cuboctahedron, the axis passing through the center of the cuboctahedron and the center of the square, and the axis passing through the center of the cuboctahedron and the center of the equilateral triangle. After the six sets of connecting curves are projected through the center of the sphere, the sphere is divided into six congruent spherical pieces, and the outer contour of the spherical pieces has the outer shape characteristics of an octopus.

[0031] The technical effects thereof are as follows. The spherical puzzle can be formed by joining six congruent pieces having the outer shape characteristics of an octopus.

[0032] Preferably, the spherical puzzle is a lizard spherical puzzle. The puzzle is designed based on the surface structure characteristics of a cuboctahedron. On the square faces of the cuboctahedron, a first set of curves having rotational symmetry of 90 degrees with respect to the center of the face is provided. On the equilateral triangle faces of the cuboctahedron, a second set of curves having rotational symmetry of 120 degrees with respect to the center of the face is provided. The first set of curves and the second set of curves are connected end to end on the surface of the cuboctahedron to form 48 sets of connecting curves. Each of the 48 sets of connecting curves has rotational symmetry of 180 degrees, 90 degrees, and 120 degrees respectively with respect to the axis passing through the center and vertices of the cuboctahedron, the axis passing through the center of the cuboctahedron and the center of the square, and the axis passing through the center of the cuboctahedron and the center of the equilateral triangle. After the 48 sets of connecting curves are projected through the center of the sphere, the sphere is divided into two types, a total of 48 spherical pieces. Each type of spherical piece has a total of 24 congruent pieces. The outer contour shapes of the two types of spherical pieces both have the outer shape characteristics of a lizard.

[0033] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 48 congruent pieces, each possessing the external characteristics of two different types of lizards.

[0034] Preferably, the spherical puzzle is a cowboy spherical puzzle, the puzzle is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves, the provided set of curves, after being rotated by an integer multiple of 72 degrees around the center of the regular pentagon, form 12 sets of connecting curves that connect the surfaces of the regular dodecahedron, the connecting curves, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a cowboy, and the spherical puzzle joined by the 12 cowboy pieces has 120 degrees of rotational symmetry with respect to the elbow and heel of the cowboy.

[0035] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 12 congruent pieces that have the external characteristics of a cowboy.

[0036] Preferably, the spherical puzzle is a robust boy's spherical puzzle, the puzzle is designed based on the surface structure features of a cuboctahedron, the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first and second sets of curves are arranged on the polygonal surfaces of the cuboctahedron. The tails are connected to form 24 sets of interconnected curves, each of which has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 24 sets of interconnected curves are projected through the center of the sphere, dividing the sphere into 24 congruent spherical pieces, and the outer contours of these spherical pieces have the contour features of a human figure.

[0037] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external characteristics of a human figure.

[0038] Preferably, the spherical puzzle is a cool man's spherical puzzle, the puzzle is designed based on the surface structure features of a regular cube, the square faces of the regular cube are provided with a set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular cube to form 24 sets of interconnected curves, each of the 24 sets of interconnected curves having 120 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular cube, an axis passing through the center of the regular cube and the center of the square, and an axis passing through the center of the regular cube and the midpoint of the edge of the square, and the 24 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 24 congruent spherical pieces, the outer contours of the spherical pieces having the external features of a cool man.

[0039] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external features of a handsome man.

[0040] Preferably, the spherical puzzle is a goat's spherical puzzle, the puzzle is designed based on the surface structure features of a cuboctahedron, the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first and second sets of curves are aligned on the polygonal surfaces of the cuboctahedron. The 24 interconnected curves are connected to form 24 sets of interconnected curves, each of which has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 24 interconnected curves are projected through the center of the sphere, dividing the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a goat.

[0041] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external characteristics of a goat.

[0042] Preferably, the spherical puzzle is a frog spherical puzzle, the puzzle is designed based on the surface structure features of a cuboctahedron, the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are coherently connected on the surface of the cuboctahedron. This forms 24 sets of interconnected curves, each of which has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 24 sets of interconnected curves are projected through the center of the sphere, dividing the sphere into 24 congruent spherical pieces, and the outer contours of these spherical pieces have the external features of a frog.

[0043] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external characteristics of a frog.

[0044] Preferably, the spherical puzzle is a singing frog spherical puzzle, the puzzle is designed based on the surface structure features of a regular octahedron, the equilateral triangular faces of the regular octahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular octahedron to form 24 sets of interconnected curves, each of the 24 sets of interconnected curves having 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular octahedron and the midpoint of the edge of the equilateral triangle, an axis passing through the center of the regular octahedron and the vertex, and an axis passing through the center of the regular octahedron and the center of the equilateral triangle, the 24 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 24 congruent spherical pieces, the outer contours of the spherical pieces having the external features of a singing frog.

[0045] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 24 congruent pieces that have the external features of a singing frog.

[0046] Preferably, the spherical puzzle is a butterfly spherical puzzle, which is designed based on the surface structure features of a regular dodecahedron, and the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the set of curves connects on the surface of the regular dodecahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves having 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and a vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and after the 60 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a butterfly.

[0047] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 60 congruent pieces that have the external characteristics of a butterfly.

[0048] Preferably, the spherical puzzle is a spherical puzzle of a dog, and the puzzle is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular dodecahedron to form 60 sets of interconnected curves, the 60 sets of interconnected curves have 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and the vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and after the 60 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a dog.

[0049] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 60 congruent pieces that have the external characteristics of a dog.

[0050] Preferably, the spherical puzzle is a Joker spherical puzzle, the puzzle is designed based on the surface structure features of a regular icosahedron, the equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular icosahedron to form 60 sets of interconnected curves, the 60 sets of interconnected curves have 72 degrees of rotational symmetry, 180 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular icosahedron, an axis passing through the center and midpoints of the edges of the equilateral triangles, and an axis passing through the center and center of the equilateral triangles, the 60 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 60 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a Joker.

[0051] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 60 congruent pieces that have the distinctive shape of a joker.

[0052] Preferably, the spherical puzzle is a lizard spherical puzzle, the puzzle is designed based on the surface structure features of a regular icosahedron, the equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular icosahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves having 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular icosahedron and the midpoint of the edges of the equilateral triangles, an axis passing through the center of the regular icosahedron and the vertices, and an axis passing through the center of the regular icosahedron and the center of the equilateral triangles, the 60 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 60 congruent spherical pieces, the outer contours of the spherical pieces having the external features of a lizard.

[0053] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 60 congruent pieces that have the external characteristics of a lizard.

[0054] Preferably, the spherical puzzle is a cat-shaped spherical puzzle, the puzzle is designed based on the surface structure features of a truncated dodecahedron, the regular pentagonal faces of the truncated dodecahedron are provided with a first set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the equilateral triangular faces of the truncated dodecahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are coherently connected on the surface of the truncated dodecahedron. This forms 60 sets of interconnected curves, each of which has 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the truncated dodecahedron, an axis passing through the center of the truncated dodecahedron and the center of the regular pentagon, and an axis passing through the center of the truncated dodecahedron and the center of the equilateral triangle. After projecting the 60 sets of interconnected curves through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the outline characteristics of a cat.

[0055] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 60 congruent pieces that have the external characteristics of a cat.

[0056] Preferably, the spherical puzzle is a lizard spherical puzzle, the puzzle is designed based on the surface structure features of a cuboctahedron, the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the first set of curves and the second set of curves are connected on the surface of the cuboctahedron to form 72 sets of interconnected curves, the 72 Each pair of interconnected curves has rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. After projecting the 72 pairs of interconnected curves through the center of the sphere, the sphere is divided into three types, totaling 72 spherical pieces. Each type of spherical piece consists of 24 congruent pieces, and the outer contour shapes of the three types of spherical pieces all have the external features of a lizard.

[0057] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 72 congruent pieces, each possessing the distinctive external features of three different types of lizards.

[0058] Preferably, the spherical puzzle is a duckbill spherical puzzle, the puzzle is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular dodecahedron to form 30 sets of interconnected curves, each of the 30 sets of interconnected curves having 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and a vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and the 30 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 30 congruent spherical pieces, the outer contours of the spherical pieces having the external features of a duckbill.

[0059] The resulting technical effect is as follows: The spherical puzzle can be formed by joining together 30 congruent pieces that have the external features of a duckbill. [Brief explanation of the drawing]

[0060] [Figure 1] This is a schematic diagram of Embodiment 1 of the spherical tiling puzzle of the present invention. [Figure 2] This is a schematic diagram of Embodiment 2 of the spherical tiling puzzle of the present invention. [Figure 3] This is a schematic diagram of Embodiment 3 of the spherical tiling puzzle of the present invention. [Figure 4] This is a schematic diagram of Embodiment 4 of the spherical tiling puzzle of the present invention. [Figure 5] This is a schematic diagram of Embodiment 5 of the spherical tiling puzzle of the present invention. [Figure 6] This is a schematic diagram of Embodiment 6 of the spherical tiling puzzle of the present invention. [Figure 7] This is a schematic diagram of Embodiment 7 of the spherical tiling puzzle of the present invention. [Figure 8] This is a schematic diagram of Embodiment 8 of the spherical tiling puzzle of the present invention. [Figure 9] This is a schematic diagram of Embodiment 9 of the spherical tiling puzzle of the present invention. [Figure 10] This is a schematic diagram of Example 10 of the spherical tiling puzzle of the present invention. [Figure 11] This is a schematic diagram of Embodiment 11 of the spherical tiling puzzle of the present invention. [Figure 12] This is a schematic diagram of Example 12 of the spherical tiling puzzle of the present invention. [Figure 13] This is a schematic diagram of Embodiment 13 of the spherical tiling puzzle of the present invention. [Figure 14] This is a schematic diagram of Embodiment 14 of the spherical tiling puzzle of the present invention. [Figure 15] This is a schematic diagram of Example 15 of the spherical tiling puzzle of the present invention. [Figure 16] This is a schematic diagram of Embodiment 16 of the spherical tiling puzzle of the present invention. [Figure 17] This is a schematic diagram of Embodiment 17 of the spherical tiling puzzle of the present invention. [Figure 18] This is a schematic diagram of Embodiment 18 of the spherical tiling puzzle of the present invention. [Figure 19] This is a schematic diagram of Embodiment 19 of the spherical tiling puzzle of the present invention. [Figure 20] This is a schematic diagram of Example 20 of the spherical tiling puzzle of the present invention. [Figure 21] This is a schematic diagram of Example 21 of the spherical tiling puzzle of the present invention. [Figure 22] This is a schematic diagram of Example 22 of the spherical tiling puzzle of the present invention. [Figure 23] This is a schematic diagram of Example 23 of the spherical tiling puzzle of the present invention. [Figure 24] This is a schematic diagram of Example 24 of the spherical tiling puzzle of the present invention. [Figure 25] This is a schematic diagram of Example 25 of the spherical tiling puzzle of the present invention. [Figure 26] This is a schematic diagram of Example 26 of the spherical tiling puzzle of the present invention. [Figure 27] This is a schematic diagram of Example 27 of the spherical tiling puzzle of the present invention. [Figure 28] This is a schematic diagram of Example 28 of the spherical tiling puzzle of the present invention. [Figure 29] This is a schematic diagram of Example 29 of the spherical tiling puzzle of the present invention. [Figure 30] This is a schematic diagram of Example 30 of the spherical tiling puzzle of the present invention. [Figure 31] This is a schematic diagram of Embodiment 31 of the spherical tiling puzzle of the present invention. [Figure 32] This is a schematic diagram of Example 32 of the spherical tiling puzzle of the present invention. [Figure 33] This is a schematic diagram of Embodiment 33 of the spherical tiling puzzle of the present invention. [Figure 34] This is a schematic diagram of Embodiment 34 of the spherical tiling puzzle of the present invention. [Figure 35] This is a schematic diagram of Example 35 of the spherical tiling puzzle of the present invention. [Figure 36] This is a schematic diagram of Embodiment 36 of the spherical tiling puzzle of the present invention. [Figure 37]This is a schematic diagram of Embodiment 37 of the spherical tiling puzzle of the present invention. [Figure 38] This is a schematic diagram of Embodiment 38 of the spherical tiling puzzle of the present invention. [Figure 39] This is a schematic diagram of Embodiment 39 of the spherical tiling puzzle of the present invention. [Figure 40] This is a schematic diagram 1 of Example 40 of the spherical tiling puzzle of the present invention. [Figure 41] This is a schematic diagram 2 of Example 40 of the spherical tiling puzzle of the present invention. [Figure 42] This is a schematic diagram of Embodiment 41 of the spherical tiling puzzle of the present invention. [Figure 43] This is a part view of Embodiment 41 of the spherical tiling puzzle of the present invention. [Figure 44] This is a schematic diagram 1 of Example 42 of the spherical tiling puzzle of the present invention. [Figure 45] This is a schematic diagram 2 of Example 42 of the spherical tiling puzzle of the present invention. [Figure 46] This is a schematic diagram of Embodiment 43 of the spherical tiling puzzle of the present invention. [Figure 47] This is a schematic diagram of Embodiment 44 of the spherical tiling puzzle of the present invention. [Figure 48] This is a schematic diagram of Embodiment 45 of the spherical tiling puzzle of the present invention. [Figure 49] This is a schematic diagram of Embodiment 46 of the spherical tiling puzzle of the present invention. [Figure 50] This is a schematic diagram of Embodiment 47 of the spherical tiling puzzle of the present invention. [Figure 51] This is a schematic diagram of Embodiment 48 of the spherical tiling puzzle of the present invention. [Figure 52] This is a schematic diagram of Embodiment 49 of the spherical tiling puzzle of the present invention. [Figure 53] This is a schematic diagram of Example 50 of the spherical tiling puzzle of the present invention. [Figure 54] This is a schematic diagram of Embodiment 51 of the spherical tiling puzzle of the present invention. [Figure 55] This is a schematic diagram of Example 52 of the spherical tiling puzzle of the present invention. [Figure 56] This is a schematic diagram of Embodiment 53 of the spherical tiling puzzle of the present invention. [Figure 57] This is a schematic diagram of Embodiment 54 of the spherical tiling puzzle of the present invention. [Figure 58] This is a schematic diagram of Example 55 of the spherical tiling puzzle of the present invention. [Figure 59] This is a schematic diagram of Embodiment 56 of the spherical tiling puzzle of the present invention. [Figure 60] This is a schematic diagram of Embodiment 57 of the spherical tiling puzzle of the present invention.

[0061] 1. Spherical regular polygon piece, 2. Notch, 3. Convex part, 4. Side edge, 5. Connecting curve. [Modes for carrying out the invention]

[0062] The technical concepts in the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments, and it will be clear that the embodiments described are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art without creative work based on the embodiments of the present invention are all within the scope of protection of the present invention.

[0063] Figures 1 to 37 of the present invention represent combinations of the first series of the present invention, and Figures 38 to 61 represent combinations of the second series of the present invention.

[0064] In the first series, the puzzle includes multiple types of spherical regular polygonal pieces, the spherical regular polygonal pieces having the same or different number of sides, and the spherical regular polygonal pieces fit together along notches or protrusions on their sides to form a hollow sphere, including two types of situations. For example, a sphere having the symmetry of a regular cube (4.4.4) may be formed by joining together six spherical regular square pieces, each having one notch or protrusion at the midpoint of one side (see Figure 19), or by joining together six spherical regular square pieces, each having a pair of notches and protrusions on its sides that have 180 degrees of rotational symmetry with respect to the midpoint of the side (see Figure 2).

[0065] The first series includes five regular polyhedra and thirteen Archimedean solids, and can be divided into two situations in total.

[0066] In the first scenario, the side of the spherical regular polygon piece is provided with a pair of notches 2 and protrusions 3 having 180 degrees of rotational symmetry with respect to the midpoint of the side. During joining, by aligning the side of the spherical regular polygon piece, the notches 2 and protrusions 3 on the side of the piece are precisely aligned and interlocked, joining to the sphere, as shown in Figures 1-18.

[0067] When a first and second connecting structure are simultaneously provided on the side of a spherical regular polygon piece, the first and second connecting structures form 180-degree rotational symmetry with respect to the midpoint of the side. Furthermore, the side on which the first and second connecting structures are provided forms rotational symmetry with respect to the center of the spherical regular polygon piece, and such a design ensures the interlocking versatility of the joint of the spherical regular polygon piece.

[0068] In the second scenario, only one connecting structure is provided at the midpoint of the side edge of the spherical regular polygon piece, and the connecting structure may be the shape of a notch 2 or a protrusion 3. During joining, by aligning the sides of the spherical regular polygon piece, the notches 2 and protrusions 3 provided at the midpoint of the side edges of adjacent pieces align and interlock precisely, joining to the sphere, as shown in Figures 19-37. Specifically, during joining, two spherical regular polygons, each with a first connecting structure (notch 2) and a second connecting structure (protrusion 3) at the midpoint of their side edges, fit together along their sides, align, and interlock. It is necessary to clarify that the total number of notches 2 on the spherical regular polygon piece used must be equal to the total number of notches 3, which ensures that the notches and protrusions of the polygon piece fit together and interlock to form a stable structure.

[0069] During joining, the types, quantities, and combinations of spherical regular polygon pieces used correspond one-to-one with the types, quantities, and combinations of regular polygons in the five regular polyhedra or thirteen Archimedean bodies. It can be understood that by replacing the polygonal surfaces of the five types of regular polyhedra or thirteen Archimedean bodies with spherical regular polygon pieces that have appropriate connecting structures on their sides, they can be joined to the corresponding spherical puzzles.

[0070] Referring to Figure 1, Embodiment 1 is a spherical puzzle (3.3.3) composed of four spherical equilateral triangular pieces, and the sides of the pieces are provided with notches and convex structures. Referring to Figure 2, Embodiment 2 is a spherical puzzle (4.4.4) composed of six spherical square pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 3, Embodiment 3 is a spherical puzzle (3.3.3.3) composed of eight spherical equilateral triangle pieces, and the difference from Embodiment 1 is that the number of spherical equilateral triangle pieces has increased. Referring to Figure 4, Embodiment 4 is a spherical puzzle (5.5.5) composed of 12 spherical regular pentagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 5, Embodiment 5 is a spherical puzzle (3.3.3.3.3) composed of 20 spherical equilateral triangle pieces, and the difference from Embodiment 3 is that the number of spherical equilateral triangle pieces has increased. Referring to Figure 6, Embodiment 6 is a spherical puzzle (3.4.3.4) composed of eight spherical equilateral triangle pieces and six spherical square pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 7, Embodiment 7 is a spherical puzzle (3.5.3.5) composed of 20 spherical equilateral triangle pieces and 12 spherical regular pentagon pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 8, Embodiment 8 is a spherical puzzle (3.6.6) composed of four spherical equilateral triangle pieces and four spherical regular hexagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 9, the embodiment 9 is a spherical puzzle (3.8.8) composed of eight spherical equilateral triangular pieces and six spherical regular octagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 10, the embodiment 10 is a spherical puzzle (4.6.6) composed of six spherical square pieces and eight spherical hexagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 11, Embodiment 11 is a spherical puzzle (3.4.4.4) composed of eight spherical equilateral triangle pieces and eighteen spherical square pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 12, Embodiment 12 is a spherical puzzle (4.6.8) composed of 12 spherical square pieces, 8 spherical hexagonal pieces, and 6 spherical octagonal pieces, with notches and protrusions provided on the sides of the pieces. Referring to Figure 13, Embodiment 13 is a spherical puzzle (3.3.3.3.4) composed of 32 spherical equilateral triangle pieces and 6 spherical square pieces, with notches and protrusions provided on the sides of the spherical regular polygon pieces, and a different joining combination than Embodiments 6 and 11. Referring to Figure 14, Embodiment 14 is a spherical puzzle (5.6.6) composed of 12 spherical pentagonal pieces and 20 spherical hexagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 15, the embodiment 15 is a spherical puzzle (3.4.5.4) composed of 20 spherical equilateral triangle pieces, 30 spherical square pieces, and 12 spherical pentagon pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 16, the embodiment 16 is a spherical puzzle (3.3.3.3.5) composed of 80 spherical equilateral triangle pieces and 12 spherical regular pentagon pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 17, Embodiment 17 is a spherical puzzle (4.6.10) composed of 30 spherical square pieces, 20 spherical hexagonal pieces, and 12 spherical decagonal pieces, with notches and convex structures provided on the sides of the pieces. Referring to Figure 18, the embodiment 18 is a spherical puzzle (3.10.10) composed of 20 spherical equilateral triangle pieces and 12 spherical regular decagonal pieces, with notches and convex structures provided on the sides of the pieces. A common feature of Examples 1 to 18 is that each side of the spherical regular polygon piece is provided with two connecting structures (notches and protrusions), and these two connecting structures (notches and protrusions) have 180 degrees of rotational symmetry with respect to the midpoint of the corresponding side. Referring to Figure 19, Embodiment 19 is a schematic diagram of the structure of a joined spherical puzzle made of six identical spherical square pieces (4.4.4), in which a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 20, the embodiment 20 is a spherical puzzle (4.6.6) composed of six spherical square pieces and eight spherical hexagonal pieces, and each piece has a notch or convex structure at the midpoint of its side edge. Referring to Figure 21, the embodiment 21 is a spherical puzzle (4.6.8) composed of 12 spherical square pieces, 8 spherical hexagonal pieces, and 6 spherical octagonal pieces, and each piece has a notch or convex structure at the midpoint of its side edge. Referring to Figure 22, Embodiment 22 is a spherical puzzle (4.6.10) composed of 30 spherical square pieces, 20 spherical hexagonal pieces, and 12 spherical decagonal pieces, with a notch or convex structure provided at the midpoint of the side edge of each piece. Referring to Figure 23, the embodiment 23 is a spherical puzzle (3.8.8) composed of eight spherical equilateral triangle pieces and six spherical regular octagonal pieces, and each piece has a notch or convex structure at the midpoint of its side edge. Referring to Figure 24, the embodiment 24 is a spherical puzzle (3.4.5.4) composed of 20 spherical equilateral triangle pieces, 30 spherical square pieces, and 12 spherical pentagon pieces, and each piece has a notch or convex structure at the midpoint of its side edge. Referring to Figure 25, the embodiment 25 is a spherical puzzle (3.4.3.4) composed of eight spherical equilateral triangle pieces and six spherical square pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 26, the embodiment 26 is a spherical puzzle (3.5.3.5) composed of 20 spherical equilateral triangle pieces and 30 spherical regular pentagon pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 27, the embodiment 27 is a spherical puzzle (5.6.6) composed of 12 spherical pentagonal pieces and 20 spherical hexagonal pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 28, Embodiment 28 is also a spherical puzzle (5.6.6) composed of 12 spherical pentagonal pieces and 20 spherical hexagonal pieces, with only one notch or protrusion provided at the midpoint of the side edge of each spherical polygonal piece. Compared to Embodiment 27, the layout method of the connection structure on the side edge of each spherical polygonal piece is different. Referring to Figure 29, Embodiment 29 is a spherical puzzle (3.3.3.3.4) composed of 32 spherical equilateral triangle pieces and 6 spherical square pieces, with only one notch or protrusion provided at the midpoint of the side edge of each spherical regular polygon piece. Compared to Embodiment 13, the layout method of the joining and connecting structure is different. Referring to Figure 30, the embodiment 30 is a spherical puzzle (3.3.3.3) composed of eight spherical equilateral triangular pieces, in which a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 31, the embodiment 31 is a spherical puzzle (5.5.5) composed of 12 spherical regular pentagonal pieces, in which a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 32, the embodiment 32 is a spherical puzzle (3.3.3.3.3) composed of 20 spherical equilateral triangular pieces, in which a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 33, the embodiment 33 is a spherical puzzle (3.6.6) consisting of four spherical equilateral triangular pieces and four spherical regular hexagonal pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 34, the embodiment 34 is a spherical puzzle (3.4.4.4) consisting of eight spherical equilateral triangle pieces and eighteen spherical square pieces, with a notch or convex structure provided at the midpoint of the side edge of each piece. Referring to Figure 35, the embodiment 35 is a spherical puzzle (3.3.3.3.4) consisting of 32 spherical equilateral triangle pieces and 6 spherical square pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 36, the embodiment 36 is a spherical puzzle (3.10.10) consisting of 20 spherical equilateral triangle pieces and 12 spherical regular decagonal pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. Referring to Figure 37, the embodiment 37 is a spherical puzzle (3.3.3.3.5) consisting of 80 spherical equilateral triangle pieces and 12 spherical regular pentagon pieces, and a notch or convex structure is provided at the midpoint of the side edge of the piece. A common feature of Examples 19-37 is that each spherical regular polygon piece in the spherical puzzle has only one connecting structure (notch or protrusion) at the midpoint of its side edge, and the total number of protrusions and notches in the spherical puzzle is equal.

[0071] As needs to be explained in the above embodiments, the first and second connection structures are not limited to notches and protrusions, but may be other interlocking structures.

[0072] As needs to be explained in the examples of the series described above, in the central projection correspondence, the types, number, and combinations of spherical regular polygon pieces in the first series of spherical puzzles correspond one-to-one with five types of regular polyhedra or thirteen types of Archimedean solids, respectively, and therefore, the sides of all spherical regular polygon pieces are equal.

[0073] Example 38 is a spherical dog puzzle, referring to Figure 38, which is designed based on the surface structure features of a cuboctahedron, with a first set of curves on the square faces of the cuboctahedron having 90 degrees of rotational symmetry with respect to the center of the face, and a second set of curves on the triangular faces of the cuboctahedron having 120 degrees of rotational symmetry with respect to the center of the face, and the first and second sets of curves each having 180 degrees of rotational symmetry with respect to the vertices of the cuboctahedron, and the first and second sets of curves The set of curves connects at the polygonal surface of the cuboctahedron to form 24 sets of interconnected curves 5, each of the 24 sets of interconnected curves 5 having 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The interconnected curves 5, when projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, the outer contours of which have the external features of a dog.

[0074] Example 39 is a spherical puzzle of a dancing man, referring to Figure 39. The puzzle is designed based on the surface structure features of a regular dodecahedron, with the same set of curves provided for the 12 regular pentagons of the dodecahedron. The set of curves of the regular pentagons, after being rotated by an integer multiple of 72° along the center, form a coherent connecting curve, referring to Figure 39. In Figure 39, when the curve on edge CD is rotated 120 degrees from point C to edge CB, and the curve on edge AB is rotated 120 degrees from point A to edge AE, the curves on the spherical pentagon ABCDE and its five adjacent spherical pentagons form exactly 12 pairs of congruent interconnected curves 5. After the interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 12 spherical pieces. The outer contours of the spherical pieces have the external features of a dancing man, and the sphere joined by the 12 pieces of the dancing man features has 120 degrees of rotational symmetry with respect to the axis passing through the intersection of the center of the dodecahedron and the three hands, and the axis passing through the intersection of the center of the dodecahedron and the three feet.

[0075] Example 40 is a spherical puzzle of a person riding a donkey, referring to Figures 40-41. The puzzle is designed based on the surface structure features of a regular octahedron. Four non-adjacent equilateral triangular faces of the regular octahedron are provided with a first set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face. The other four non-adjacent equilateral triangular faces of the regular octahedron are provided with a second set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face. The first and second sets of similar curves are connected on the surface of the regular octahedron to form 12 sets of connecting curves 5. Each of the 12 sets of connecting curves 5 has 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular octahedron, an axis passing through the center and the centers of the equilateral triangles, and 120 degrees of rotational symmetry. The 12 sets of connecting curves 5, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a person riding a donkey.

[0076] Example 41 is a butterfly spherical puzzle, referring to Figure 42. The puzzle is designed based on the surface structure features of a regular cube. The quadrilateral faces of the regular cube are provided with a set of curves having 90 degrees of rotational symmetry with respect to the center of the face. The curve sets are connected on the polygonal surfaces of the regular cube to form 24 sets of interconnected curves 5. Each of the 24 sets of interconnected curves has 120 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular cube, an axis passing through the center of the regular cube and the center of the quadrilateral, and an axis passing through the center of the regular cube and the midpoint of the edge of the quadrilateral. After the 24 sets of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a butterfly.

[0077] Figure 43 shows the actual state of Example 41.

[0078] Example 42 is a rabbit spherical puzzle, referring to Figures 44-45, the puzzle is designed based on the surface structure features of a regular octahedron, with four non-adjacent equilateral triangular faces of the regular octahedron having a first set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and the other four non-adjacent equilateral triangular faces of the regular octahedron having a second set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of similar curves and the second set of similar curves These connect on the surface of the regular octahedron to form 12 sets of interconnected curves 5, each of which has 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and mirror symmetry with respect to an axis passing through the center and vertices of the regular octahedron, an axis passing through the center of the regular octahedron and the center of the equilateral triangle, and a plane passing through the center of the regular octahedron and the edge of the equilateral triangle. The 12 sets of interconnected curves 5, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a rabbit.

[0079] Example 43 is an octopus spherical puzzle, referring to Figure 46, which is designed based on the surface structure features of a cuboctahedron, wherein the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are aligned on the surface of the cuboctahedron. Subsequently, six sets of interconnected curves 5 are formed, each of which has 180-degree rotational symmetry, 90-degree rotational symmetry, and 120-degree rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. After the six sets of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into six congruent spherical pieces, and the outer contours of these spherical pieces have the external features of an octopus.

[0080] Example 44 is a lizard spherical puzzle, referring to Figure 47, which is designed based on the surface structure features of a cuboctahedron, where the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected on the surface of the cuboctahedron to form 48 sets of interconnected curves 5, and 48 sets Each of the 5 interconnected curves has rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 48 sets of interconnected curves 5 are projected through the center of the sphere, dividing the sphere into two different types of spherical pieces. Each type of spherical piece consists of 24 congruent pieces, and the outer contour shapes of these two types of spherical pieces all have the external features of a lizard.

[0081] Example 45 is a cowboy spherical puzzle, referring to Figure 48, which is designed based on the surface structure features of a regular dodecahedron, where a set of curves is provided on the regular pentagonal faces of the dodecahedron, and after the set of curves is rotated by a multiple of 72 degrees around the center of the regular pentagon, it forms 12 sets of connecting curves 5 that connect the dodecahedron's surface, and after the connecting curves 5 are projected through the center of the sphere, the sphere is divided into 12 congruent spherical pieces, the outer contours of the spherical pieces having cowboy features, and the sphere joined by the 12 cowboy feature pieces has 120 degrees of rotational symmetry with respect to the axis passing through the intersection of the center of the dodecahedron and the three elbows, and the axis passing through the intersection of the center of the dodecahedron and the three heels.

[0082] Example 46 is a robust boy's spherical puzzle, referring to Figure 49, which is designed based on the surface structure features of a cuboctahedron, with the square faces of the cuboctahedron having a first set of curves with 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron having a second set of curves with 120 degrees of rotational symmetry with respect to the center of the face, and the first and second sets of curves are arranged on the surface of the cuboctahedron The tails are connected to form 24 sets of interconnected curves 5, each interconnected curve 5 having 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 24 sets of interconnected curves 5 are projected through the center of the sphere, dividing the sphere into 24 congruent spherical pieces, each of which has the outline features of a human figure.

[0083] Example 47 is a cool man's spherical puzzle, and referring to Figure 50, the puzzle is designed based on the surface structure features of a regular cube, and the square faces of the regular cube are provided with a set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the set of curves is connected on the polygonal surfaces of the regular cube to form 24 sets of interconnected curves 5, each of the 24 sets of interconnected curves 5 having 120 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular cube, an axis passing through the center of the regular cube and the center of the square, and an axis passing through the center of the regular cube and the midpoint of the edge of the square, respectively, and after these 24 sets of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 24 congruent spherical pieces, and the spherical pieces have the outline features of a human figure.

[0084] Example 48 is a goat's spherical puzzle, referring to Figure 51, which is designed based on the surface structure features of a cuboctahedron, with a first set of curves on the square faces of the cuboctahedron having 90 degrees of rotational symmetry with respect to the center of the face, and a second set of curves on the triangular faces of the cuboctahedron having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are coherently connected on the surface of the cuboctahedron. This forms 24 sets of interconnected curves 5, each interconnected curve 5 having 180-degree rotational symmetry, 90-degree rotational symmetry, and 120-degree rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 24 sets of interconnected curves 5, after being projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, and the outer contours of these spherical pieces have the distinctive features of a robust goat.

[0085] Example 49 is a frog spherical puzzle, referring to Figure 52, which is designed based on the surface structure features of a cuboctahedron, with a first set of curves on the square faces of the cuboctahedron having 90 degrees of rotational symmetry with respect to the center of the face, and a second set of curves on the triangular faces of the cuboctahedron having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are coherently connected on the surface of the cuboctahedron. These form 24 sets of interconnected curves 5, each interconnected curve 5 having 180-degree rotational symmetry, 90-degree rotational symmetry, and 120-degree rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. These 24 sets of interconnected curves 5, when projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, and the outer contours of these spherical pieces have the external features of a frog.

[0086] Example 50 is a spherical puzzle of a singing frog, and referring to Figure 53, the puzzle is designed based on the surface structure features of a regular octahedron, and the equilateral triangular faces of the regular octahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the set of curves connects on the surface of the regular octahedron to form 24 sets of connecting curves 5, each of the 24 sets of connecting curves 5 having 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular octahedron and the midpoint of the edge of the equilateral triangle, an axis passing through the center of the regular octahedron and the vertex, and an axis passing through the center of the regular octahedron and the center of the equilateral triangle, respectively, and after the 24 sets of connecting curves 5 are projected through the center of the sphere, the sphere is divided into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a singing frog.

[0087] Example 51 is a butterfly spherical puzzle, referring to Figure 54. The puzzle is designed based on the surface structure features of a regular dodecahedron. The regular pentagonal faces of the dodecahedron are provided with a set of curves having 72 degrees of rotational symmetry with respect to the center of the face. The curve sets are connected on the surface of the dodecahedron to form 60 sets of interconnected curves 5. Each of the 60 sets of interconnected curves 5 has 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the dodecahedron and the midpoint of the edge of the pentagon, an axis passing through the center of the dodecahedron and a vertex, and an axis passing through the center of the dodecahedron and the center of the pentagon. After the 60 sets of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, the outer contours of which have the external features of a butterfly.

[0088] Example 52 is a spherical dog puzzle, referring to Figure 55. The puzzle is designed based on the surface structure features of a regular dodecahedron, and the regular pentagonal faces of the dodecahedron are provided with a set of curves having 72 degrees of rotational symmetry with respect to the center of the face. The set of curves connects on the surface of the dodecahedron to form 60 pairs of interconnected curves 5. Each of the 60 pairs of interconnected curves 5 has 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the dodecahedron and the midpoint of the edge of the pentagon, an axis passing through the center of the dodecahedron and a vertex, and an axis passing through the center of the dodecahedron and the center of the pentagon. After projecting these 60 pairs of interconnected curves 5 through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a dog.

[0089] Example 53 is a Joker spherical puzzle, referring to Figure 56. The puzzle is designed based on the surface structure features of a regular icosahedron. The equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face. These curve sets are connected on the surface of the regular icosahedron to form 60 sets of interconnected curves 5. Each of the 60 sets of interconnected curves 5 has 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular icosahedron and the midpoint of the edges of the equilateral triangles, an axis passing through the center of the regular icosahedron and the vertices, and an axis passing through the center of the regular icosahedron and the center of the equilateral triangles. These 60 sets of interconnected curves 5 are projected through the center of the sphere, dividing the sphere into 60 congruent spherical pieces, the outer contours of which have the external features of a Joker.

[0090] Example 54 is a lizard spherical puzzle, referring to Figure 57. The puzzle is designed based on the surface structure features of a regular icosahedron. The equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face. The curve sets are connected on the surface of the regular icosahedron to form 60 pairs of interconnected curves 5. Each of the 60 pairs of interconnected curves 5 has 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular icosahedron and the midpoint of the edges of the equilateral triangles, an axis passing through the center of the regular icosahedron and the vertices, and an axis passing through the center of the regular icosahedron and the center of the equilateral triangles. After the 60 pairs of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, the outer contours of which have the external features of a lizard.

[0091] Example 55 is a spherical cat puzzle, referring to Figure 58, which is designed based on the surface structure features of a truncated dodecahedron, where the regular pentagonal faces of the truncated dodecahedron are provided with a first set of curves having 72 degrees of rotational symmetry with respect to the center of the face, and the equilateral triangular faces of the truncated dodecahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are coherently connected on the surface of the truncated dodecahedron. This forms 60 sets of interconnected curves 5, each of the 60 sets of interconnected curves having 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the truncated dodecahedron, an axis passing through the center of the truncated dodecahedron and the center of the regular pentagon, and an axis passing through the center of the truncated dodecahedron and the center of the equilateral triangle. After projecting the 60 sets of interconnected curves 5 through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of these spherical pieces have the outline characteristics of a cat.

[0092] Example 56 is a lizard spherical puzzle, referring to Figure 59. The puzzle is designed based on the surface structure features of a cuboctahedron. The square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face. The first and second sets of curves are connected on the surface of the cuboctahedron to form 72 sets of interconnected curves 5. Each of the interconnected curves 5 has rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle. The 72 sets of interconnected curves 5 are projected through the center of the sphere, dividing the sphere into three different types of spherical pieces. Each type of piece consists of 24 congruent pieces, and all three types of spherical pieces have the outline features of a lizard.

[0093] Example 57 is a duckbill spherical puzzle, referring to Figure 60, which is designed based on the surface structure features of a regular dodecahedron, with a set of curves on the regular pentagonal faces of the dodecahedron having 72 degrees of rotational symmetry with respect to the center of the face, and the set of curves connects on the surface of the dodecahedron to form 30 sets of interconnected curves 5, each interconnected curve having 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the dodecahedron and the midpoint of the edges of the pentagons, an axis passing through the center of the dodecahedron and the vertices, and an axis passing through the center of the dodecahedron and the center of the pentagons, respectively, and after the 30 sets of interconnected curves 5 are projected through the center of the sphere, the sphere is divided into 30 congruent spherical pieces, the spherical pieces having the outline features of a duckbill.

[0094] The symmetrical structure of the spherical puzzles constructed in this patent is based on five regular polyhedra or thirteen Archimedean bodies, and comprises a total of two series. The first series of spherical puzzles is further divided into two categories, comprising a total of 37 examples, and the second series of spherical puzzles comprises a total of 20 examples, which are outlined below.

[0095] The first series of spherical puzzles consists of two types, with puzzle structures corresponding to five regular polyhedra and thirteen Archimedean bodies. In the first type, each side of the spherical regular polygon piece of the spherical puzzle is provided with a pair of convex and notches, the shapes of which are the same, and the convex and notches form 180° rotational symmetry with respect to the midpoint of the side. Furthermore, the side with the convex and notches has rotational symmetry with respect to the center of the spherical regular polygon piece. In the second type, the midpoint of the side of the spherical regular polygon piece on the spherical puzzle is provided with either a single notch or a single convex to ensure that the spherical regular polygon piece in the puzzle fits and interlocks with the side during joining and that the total number of convex and notches on the spherical puzzle is equal.

[0096] The pieces of the second series of spherical puzzles have the outline appearance of human figures or animals and are designed based on the symmetry principle of regular polyhedra or Archimedean fields. Therefore, the human figure or animal pieces on the spherical puzzles form rotational or mirror symmetry of a specific angle with respect to an axis passing through the midpoint and vertices of a polyhedron, an axis passing through the midpoint of a polyhedron and the center of a regular polygon, an axis passing through the midpoint of a polyhedron and the midpoint of a side of a regular polygon, and a plane passing through the midpoint of a polyhedron and the edge of a regular polygon. Their main attributes are summarized in Table 1.

[0097] Table 1: Summary of information on 20 spherical puzzles whose pieces have the outline appearance of a human figure or animal. JPEG2026062397000002.jpg141170

[0098] Since the apparatus and methods of use disclosed in the examples correspond to the methods disclosed in the examples, their explanation is relatively straightforward, and relevant sections should be referred to in the description of the methods.

[0099] The above description of the disclosed embodiments will enable those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the invention. Accordingly, the present invention is not limited to these embodiments shown herein, but fits to the broadest extent that is consistent with the principles and novel features disclosed herein.

Claims

1. A spherical tiling puzzle characterized by comprising multiple spherical pieces, wherein the spherical pieces are arranged using spherical regular polygons as the basic design element, the multiple spherical regular polygon pieces constituting the spherical puzzle have the same or different number of sides, the multiple spherical regular polygon pieces can be joined to a hollow spherical puzzle according to the surface layout of five types of regular polyhedra or thirteen types of Archimedean bodies, and the spherical pieces, which are arranged by deforming spherical regular polygons as the basic design element, have multiple types of outer contour shapes.

2. The spherical puzzle according to claim 1, characterized in that, when the outer contour shapes of the multiple spherical pieces constituting the spherical puzzle are polygonal, a first connecting structure or a second connecting structure is provided on any side of any spherical piece, or both the first and second connecting structures are provided simultaneously, the outer contour shapes of the first connecting structure and the outer contour shapes of the second connecting structure are fitted together and joined, the multiple spherical pieces are joined to the spherical puzzle by the interlocking of the first and second connecting structures, the total number of first and second connecting structures on the sides of the multiple regular spherical polygons constituting the spherical puzzle is the same, and the lengths of the sides of the multiple regular spherical polygon pieces constituting the spherical puzzle are the same.

3. The spherical puzzle according to claim 2, characterized in that, when one connecting structure is provided on each side of any of the multiple spherical pieces constituting the spherical puzzle, the first connecting structure or the second connecting structure on the side of any spherical regular polygon piece is located at the midpoint of that side, and the first connecting structure on the side of any spherical regular polygon piece fits and joins with the second connecting structure on the side of an adjacent spherical regular polygon piece.

4. The spherical puzzle according to claim 2, characterized in that, when multiple connection structures are provided on any side of any of the multiple spherical pieces constituting the spherical puzzle, the first and second connection structures on the side of any spherical regular polygon piece have rotational symmetry with respect to the midpoint of the side, and the side of any spherical regular polygon piece forms rotational symmetry with respect to the center of the spherical piece.

5. This is a spherical dog puzzle, which is designed based on the surface structure features of a cuboctahedron, and the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected at the polygonal surfaces of the cuboctahedron to form 24 sets of interconnected curves, and the interconnected curves The spherical tiling puzzle according to claim 1, characterized in that each connecting curve has rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, respectively, and the 24 sets of connecting curves are projected through the center of the sphere to divide the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a dog.

6. A spherical puzzle of a dancing man, characterized in that the spherical puzzle of a dancing man is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves, the set of curves, after being rotated by an integer multiple of 72 degrees around the center of the regular pentagon, forms 12 sets of interconnected curves that connect properly on the surface of the regular dodecahedron, the 12 sets of interconnected curves, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a dancing man, and the spherical puzzle joined by the 12 dancing man pieces has 120 degrees of rotational symmetry with respect to the hands and feet of the dancing man.

7. This is a spherical puzzle of a person riding a donkey, and the spherical puzzle of a person riding a donkey is designed based on the surface structure features of a regular octahedron, and the four non-adjacent equilateral triangular faces of the regular octahedron are provided with a first set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and the other four non-adjacent equilateral triangular faces of the regular octahedron are provided with a second set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of similar curves and the second set of similar curves are The spherical tiling puzzle according to claim 1, characterized in that twelve sets of interconnected curves are formed by connecting them on the surface of an octahedron, each of the twelve sets of interconnected curves has 180 degrees of rotational symmetry and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular octahedron, and an axis passing through the center of the regular octahedron and the center of an equilateral triangle, respectively, and after projecting the twelve sets of interconnected curves through the center of a sphere, the sphere is divided into twelve congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a person riding a donkey.

8. A spherical puzzle of a butterfly, characterized in that the spherical puzzle of a butterfly is designed based on the surface structure features of a regular cube, the square faces of the regular cube are provided with a set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular cube to form 24 sets of interconnected curves, each of the 24 sets of interconnected curves has 120 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular cube, an axis passing through the center of the regular cube and the center of the square, an axis passing through the center of the regular cube and the midpoint of the edge of the square, and after the 24 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a butterfly, as described in claim 1.

9. This is a rabbit-shaped spherical puzzle, which is designed based on the surface structure features of a regular octahedron, wherein four non-adjacent equilateral triangular faces of the regular octahedron are provided with a first set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and four other non-adjacent equilateral triangular faces of the regular octahedron are provided with a second set of similar curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of similar curves and the second set of similar curves are coherently connected on the polygonal surface of the regular octahedron. The spherical tiling puzzle according to claim 1, characterized in that it forms 12 sets of interconnected curves, each of the 12 sets of interconnected curves having 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and mirror symmetry with respect to an axis passing through the center and vertices of a regular octahedron, an axis passing through the center of a regular octahedron and the center of an equilateral triangle, and a plane passing through the center of a regular octahedron and the edge of an equilateral triangle, and after projecting the 12 sets of interconnected curves through the center of a sphere, the sphere is divided into 12 congruent spherical pieces, and the outer contours of the spherical pieces have the external shape characteristics of a rabbit.

10. This is an octopus spherical puzzle, which is designed based on the surface structure features of a cuboctahedron, wherein the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected on the polygonal surfaces of the cuboctahedron to form six sets of interconnected curves. The spherical tiling puzzle according to claim 1, characterized in that the aforementioned connecting curves each have rotational symmetry of 180 degrees, 90 degrees, and 120 degrees with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, respectively, and the six sets of connecting curves, after being projected through the center of the sphere, divide the sphere into six congruent spherical pieces, and the outer contours of the spherical pieces have the external features of an octopus.

11. This is a lizard-shaped spherical puzzle, which is designed based on the surface structure features of a cuboctahedron, with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the square faces of the cuboctahedron, and a second set of curves having 120 degrees of rotational symmetry with respect to the center of the triangular faces of the cuboctahedron, and the first set of curves and the second set of curves are connected on the surface of the cuboctahedron to form 48 sets of interconnected curves, each of the 48 sets of interconnected curves being connected to the cuboctahedron The spherical tiling puzzle according to claim 1, characterized in that it has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the body, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, and the 48 pairs of interconnected curves are projected through the center of the sphere, after which the sphere is divided into two types, totaling 48 spherical pieces, with a total of 24 congruent spherical pieces, and the outer contour shapes of the two types of spherical pieces all have the external features of a lizard.

12. A spherical puzzle of a cowboy, characterized in that the spherical puzzle of a cowboy is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves, the set of curves, after being rotated by an integer multiple of 72 degrees around the center of the regular pentagon, forms 12 sets of interconnected curves that connect on the surface of the regular dodecahedron, the 12 sets of interconnected curves, after being projected through the center of the sphere, divide the sphere into 12 congruent spherical pieces, the outer contours of the spherical pieces have the external features of a cowboy, and the spherical puzzle joined by the 12 cowboy pieces has 120 degrees of rotational symmetry with respect to the elbow and heel of the cowboy.

13. This is a robust boy's spherical puzzle, which is designed based on the surface structure features of a cuboctahedron. The square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face. The first and second sets of curves are connected along the polygonal surfaces of the cuboctahedron to form 24 sets of interconnected curves. The spherical tiling puzzle according to claim 1, wherein each of the 24 pairs of interconnected curves has 180-degree rotational symmetry, 90-degree rotational symmetry, and 120-degree rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, and the 24 pairs of interconnected curves, after being projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a strong boy.

14. A spherical puzzle of a cool man, characterized in that the spherical puzzle of a cool man is designed based on the surface structure features of a regular cube, the square faces of the regular cube are provided with a set of curves having 90 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular cube to form 24 sets of interconnected curves, each of the 24 sets of interconnected curves having 120 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 180 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular cube, an axis passing through the center of the regular cube and the center of the square, an axis passing through the center of the regular cube and the midpoint of the edge of the square, the 24 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a cool man, as described in claim 1.

15. This is a spherical puzzle of a goat, which is designed based on the surface structure features of a cuboctahedron, wherein the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected at the polygonal surfaces of the cuboctahedron to form 24 sets of interconnected curves. The spherical tiling puzzle according to claim 1, characterized in that each of the 24 pairs of interconnected curves has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, and the 24 pairs of interconnected curves, after being projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a goat.

16. This is a spherical frog puzzle, which is designed based on the surface structure features of a cuboctahedron, wherein the square faces of the cuboctahedron are provided with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the face, and the triangular faces of the cuboctahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected at the polygonal surfaces of the cuboctahedron to form 24 sets of interconnected curves. The spherical tiling puzzle according to claim 1, characterized in that each of the 24 pairs of interconnected curves has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cuboctahedron, an axis passing through the center of the cuboctahedron and the center of the square, and an axis passing through the center of the cuboctahedron and the center of the equilateral triangle, and the 24 pairs of interconnected curves, after being projected through the center of the sphere, divide the sphere into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external shape characteristics of a frog.

17. A spherical puzzle of a singing frog, characterized in that the spherical puzzle of a singing frog is designed based on the surface structure features of a regular octahedron, the equilateral triangular faces of the regular octahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular octahedron to form 24 sets of interconnected curves, each of the 24 sets of interconnected curves has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular octahedron and the midpoint of the edge of the equilateral triangle, an axis passing through the center of the regular octahedron and the vertex, and an axis passing through the center of the regular octahedron and the center of the equilateral triangle, and after the 24 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 24 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a singing frog, as described in claim 1.

18. A spherical puzzle of a butterfly, characterized in that the spherical puzzle of a butterfly is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular dodecahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves has 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and a vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and after the 60 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a butterfly, as described in claim 1.

19. A spherical puzzle of a dog, characterized in that the spherical puzzle of the dog is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular dodecahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves has 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and a vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and after the 60 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a dog.

20. A spherical puzzle of the Joker, characterized in that the Joker spherical puzzle is designed based on the surface structure features of a regular icosahedron, the equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular icosahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves has 72 degrees of rotational symmetry, 180 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the regular icosahedron, an axis passing through the center and midpoint of the edges of the equilateral triangles, an axis passing through the center and the center of the equilateral triangles, and the spherical puzzle according to claim 1, wherein the interconnected curves of the 60 sets of interconnected curves are projected through the center of the sphere to divide the sphere into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a Joker.

21. A spherical puzzle of a lizard, characterized in that the spherical puzzle of a lizard is designed based on the surface structure features of a regular icosahedron, the equilateral triangular faces of the regular icosahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the polygonal surfaces of the regular icosahedron to form 60 sets of interconnected curves, each of the 60 sets of interconnected curves has 180 degrees of rotational symmetry, 72 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center of the regular icosahedron and the midpoint of the edge of the equilateral triangle, an axis passing through the center of the regular icosahedron and a vertex, and an axis passing through the center of the regular icosahedron and the center of the equilateral triangle, and after the 60 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a lizard.

22. This is a spherical cat puzzle, which is designed based on the surface structure features of a truncated dodecahedron, and the regular pentagonal faces of the truncated dodecahedron are provided with a first set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the equilateral triangular faces of the truncated dodecahedron are provided with a second set of curves having 120 degrees of rotational symmetry with respect to the center of the face, and the first set of curves and the second set of curves are connected on the surface of the truncated dodecahedron to form 60 sets of interconnected curves, and The spherical tiling puzzle according to claim 1, characterized in that the 60 sets of interconnected curves each have rotational symmetry of 180 degrees, 72 degrees, and 120 degrees with respect to an axis passing through the center and vertices of a truncated dodecahedron, an axis passing through the center of a truncated dodecahedron and the center of a regular pentagon, and an axis passing through the center of a truncated dodecahedron and the center of an equilateral triangle, respectively, and after projecting the 60 sets of interconnected curves through the center of a sphere, the sphere is divided into 60 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of a cat.

23. This is a lizard-shaped spherical puzzle, which is designed based on the surface structure features of a cuboctahedron, with a first set of curves having 90 degrees of rotational symmetry with respect to the center of the square faces of the cuboctahedron, and a second set of curves having 120 degrees of rotational symmetry with respect to the center of the triangular faces of the cuboctahedron, and the first set of curves and the second set of curves are connected on the surface of the cuboctahedron to form 72 sets of interconnected curves, each of the 72 sets of interconnected curves being connected to the cuboctahedron The spherical tiling puzzle according to claim 1, characterized in that it has 180 degrees of rotational symmetry, 90 degrees of rotational symmetry, and 120 degrees of rotational symmetry with respect to an axis passing through the center and vertices of the cubeoctahedron and the center of the square, and an axis passing through the center of the cubeoctahedron and the center of the equilateral triangle, and the 72 sets of connecting curves are projected through the center of the sphere to divide the sphere into three types, totaling 72 spherical pieces, with a total of 24 congruent spherical pieces in each type, and the outer contour shapes of the three types of spherical pieces all have the external features of a lizard.

24. A spherical puzzle of duckbill, characterized in that the duckbill spherical puzzle is designed based on the surface structure features of a regular dodecahedron, the regular pentagonal faces of the regular dodecahedron are provided with a set of curves having 120 degrees of rotational symmetry with respect to the center of the face, the set of curves are connected on the surface of the regular dodecahedron to form 30 sets of interconnected curves, each of the 30 sets of interconnected curves having 180 degrees of rotational symmetry, 120 degrees of rotational symmetry, and 72 degrees of rotational symmetry with respect to an axis passing through the center of the regular dodecahedron and the midpoint of the edge of the regular pentagon, an axis passing through the center of the regular dodecahedron and a vertex, and an axis passing through the center of the regular dodecahedron and the center of the regular pentagon, and after the 30 sets of interconnected curves are projected through the center of the sphere, the sphere is divided into 30 congruent spherical pieces, and the outer contours of the spherical pieces have the external features of duckbill, as described in claim 1.

Images