SPHERICAL TILING PUZZLE

Description

CROSS REFERENCE TO RELATED APPLICATIONS

The present disclosure claims the priority to the Chinese patent application with the filing NO. 2024223787326, entitled “ANIMAL OR HUMAN PORTRAIT SPHERICAL TILING SYSTEM BASED ON REGULAR POLYGON BASIC DESIGN” and filed on Sep. 29, 2024 with Chinese Patent Office and the priority to the Chinese patent application with the filing NO. 2024116593566, entitled “SPHERICAL TILING SYSTEM BASED ON REGULAR POLYGON” and filed on Nov. 20, 2024 with Chinese Patent Office, the contents of which are incorporated herein by reference in their entirety.

TECHNICAL FIELD

The present disclosure relates to the technical field of spherical tiling structures, in particular to a spherical tiling construction method of a hollow spherical puzzle.

BACKGROUND ART

Plane tiling refers to a laying method of covering a certain area on a plane, so that the entire plane is covered seamlessly without leaving white space or overlapping. As early as ancient Greece, the plane tiling has attracted people's interest, and is applied in many fields. In mathematics, the plane tiling is widely used to study geometry and topology problems. In the field of art, the plane tiling is used for designing patterns and decoration. For example, the famous Morse pattern is a plane tiling structure. In the field of engineering, the plane tiling is applied to manufacture complex structures and materials, including architectural design and textile manufacturing. Although the plane tiling is the most familiar and commonly used type of tiling, the existing patents (such as a Chinese patent CN200610065866.6 tiling plane system) mainly focus on splicing of a plane system, and cannot achieve a tiling structure on a three-dimensional level.

A spherical tiling refers to using a simply-connected spherical block to cover a sphere, without allowing overlaps or gaps. The spherical tiling may effectively divide the sphere into small areas, so that each area may be covered without gaps, and is widely used in geography, astronomy, computer graphics and other fields. For example, map projection is an application of the spherical tiling. The map is produced and used by projecting the earth's surface onto the plane. Compared with the plane tiling, the tiling in spherical space is very rare. Because the technical realization of a tiling sphere without gaps and overlaps is far more complex than that of the plane. At present, the spherical tiling reported is relatively limited, and a regular polygon is the simplest and most important tilting element.

The exiting prior spherical puzzle patents (such as Japanese patents JP2006334192A, JP2006334263A and JP3166704U) have increased the interest and complexity of the puzzle to a certain extent. However, the structures are relatively simple, and a development trend is relatively limited. These patents mainly focus on the realization of spherical puzzles by combining and splicing a plurality of regular polygons, lacking innovation and diversity.

At present, the spherical puzzles mainly appear in the toy and education markets (such as globe puzzles), with limited content and depth and low added value of products. In addition, due to relatively simple construction technology and lack of patent barriers and technological innovation of the current spherical puzzles, product vicious competition is serious.

Therefore, it is an urgent problem for those of ordinary skill in the art to solve how to construct a new type of a spherical puzzle to make it have a more flexible construction mode, a wider application environment, a richer shape structure, and a more objective economic potential, ensure that the spherical puzzle has more outstanding characteristics and competitiveness in economy, popular science and brain development, knowledge education and art, and show a broader application prospect.

SUMMARY

In view of this, the present disclosure provides a spherical tiling puzzle, which can achieve a spherical tiling of a three-dimensional level, diversified puzzle construction modes and a broader application space.

In order to achieve the foregoing objects, the present disclosure adopts the following technical solutions: a spherical tiling puzzle, including a plurality of spherical tiles. The spherical tiles are each provided with a spherical regular polygon as a basic design element, the spherical regular polygon tiles constituting a spherical puzzle have same number of sides or different numbers of sides, the plurality of spherical regular polygon tiles are configured to be spliced into the spherical puzzle according to surface layouts of five regular polyhedrons or thirteen Archimedean solids (semiregular solids), and the spherical tiles provided through deformation of the spherical regular polygons as the basic design elements have various outer contour shapes, including but not limited to polygon-like, animal-like and human-like outer contour shapes.

The beneficial effects of the present disclosure are that spherical tiles of the spherical tiling puzzle include two series, where outer contour shapes of a first series are spherical polygon-like, and outer contour shapes of a second series are animal-like and human-like spherical tiles. A common feature thereof is that the spherical tiles have the spherical regular polygons as the basic design elements. Polygon-like tiles are based on regular polygons and are structurally designed on sides of the regular polygons, and the animal-like and human-like tiles are designed based on the regular polygons, and then the corresponding deformation curves are designed on the regular polygons.

Preferably, when the outer contour shapes of the spherical tiles constituting the spherical puzzle are spherical regular polygon-like shapes, sides of the spherical regular polygon tiles are each provided with a first connecting structure or a second connecting structure or both the first connecting structure and the second connecting structure, outer contour shapes and sizes of the first connecting structure and the second connecting structure are consistent, the plurality of spherical regular polygon tiles are spliced into a ball along sides through engagement of the first connecting structures and the second connecting structures, the first connecting structures and the second connecting structures provided on the spherical regular polygon tiles in a splicing ball are equal in the total number, and the sides of the spherical regular polygon tiles constituting the spherical puzzle are equal in length.

The resulting technical effect is that the spherical puzzle is formed by splicing the plurality of spherical regular polygon tiles. These spherical regular polygon tiles may have same number of sides or different number of sides. The sides of all spherical regular polygon tiles are equal in length, ensuring that the first connecting structures and the second connecting structures on sides may be precisely aligned, adapted to and engaged with each other to be spliced into a ball. The total number of the first connecting structures on the sides of the spherical regular polygon tiles in the splicing ball are equal to the total number of the second connecting structures, ensuring that the first connecting structures and the second connecting structures may be paired and engaged to form the stable spherical puzzle.

When the outer contour shapes of the spherical tiles are various spherical regular polygon like, the connection structures on the sides of the spherical regular polygon tiles have two design solutions: in the first type, the sides of the spherical regular polygon tiles have a plurality of connecting structures, and in the second type, the sides of the spherical regular polygon tiles have only one connecting structure.

Preferably, when the plurality of connecting structures are provided on sides of regular polygon tiles constituting the spherical puzzle, the sides of the spherical regular polygon tiles are consistent in length, the first connecting structures and the second connecting structures on the sides of the tiles are consistent in shape and size, the connecting structures form 180° rotational symmetry with respect to midpoints of the sides, and sides of the spherical tile provided with the connecting structures form rotational symmetry with respect to a center of the spherical tile.

The resulting technical effect is that this solution is a first case in the first series. At this time, the sides of the spherical regular polygon tiles are consistent in length, and the first connecting structures and the second connecting structures on the sides of the tiles form the rotational symmetry of 180° with respect to the midpoints of the sides. When aligning the sides of the two pieces of the tiles, the first and second connecting structures of the spherical tiles are precisely adapted to and engage with each other, so that no matter whether the spherical regular polygon tiles are identical or not. The tiles may be precisely engaged and spliced, providing great convenience and degree of freedom.

Preferably, when the sides of the regular polygon tiles constituting the spherical puzzle is only provided with one connecting structure, the sides of the spherical regular polygon tiles are consistent in length, a first connecting structure or a second connecting structure on the side of tiles are provided at a midpoint of the side, the sides of the plurality of spherical regular polygon tiles are aligned and engaged with and adapted to each other, and the first connecting structure and the second connecting structure on sides of adjacent spherical regular polygon tiles are adapted to and spliced with each other.

The resulting technical effect is that the solution is a second case in the first series. At this time, the connecting structures are positioned at midpoints of sides of the spherical regular polygon tiles. Because the sides are consistent in length, when sides of two pieces of the tiles are aligned, the first connecting structure of the spherical tile is precisely adapted and engaged with the second connecting structure on a side of an adjacent spherical tile, so that the spherical regular polygon tiles no matter having same number of sides or different numbers of sides may be precisely engaged and spliced, providing great convenience and free of freedom.

In the foregoing two solutions, the first one is that the sides of the spherical regular polygon tiles are each provided with the first and second connecting structures having 180° rotational symmetry with respect to the midpoint of the side, and the second one is that the sides of the spherical regular polygon tiles are each provided with only one first or second connecting structure at the midpoint. The tiles whose sides are provided with such connecting structures may splice the corresponding spherical puzzle when the types, numbers and combinations of the spherical regular polygon tiles correspond one by one with the types, numbers and combinations of the regular polygons of 5 regular polyhedrons or 13 Archimedean solids.

Preferably, based on a symmetrical geometric structure of regular polyhedrons and Archimedean solids, according to contour shape characteristics of animals or humans, specific curve sets fitting symmetrical characteristics of polyhedron are designed on regular polygon surfaces of the polyhedron. The curve sets are connected head-to-tail on surfaces of the polyhedron to form a plurality of groups of connected curves. The plurality of groups of connected curves have rotational symmetry or mirror symmetry at a specific angle with respect to axes passing through a center and vertexes of the polyhedron, axes passing through the center of the polyhedron and centers of the regular polygon surfaces, or axes passing through the center of the polyhedron and midpoints of sides of the regular polygon surfaces, or planes passing through the center of the polyhedron and sides of the regular polygon surfaces. The plurality of groups of connected curves divide, after being projected through a center of a sphere, the sphere into congruent spherical tiles, and outer contours of the spherical tiles each have contour shape characteristics of an animal or a human.

The resulting technical effect is that the foregoing solution solves the problem of the second series of the spherical puzzle: the tiles constituting the spherical puzzle have outer contour characteristics of recognizable characters or animals (such as the outer contour shape of cat, dog, flower, human and the like). The constructed spherical tiles not only have characters or animals, but also meet symmetrical structures of the regular polyhedrons or Archimedean solids. The spherical tiles are flexible and changeable, closely connected with nature and people's life, and become a puzzle with artistic sense and aesthetic characteristics.

Preferably, the spherical puzzle is a puppy spherical puzzle, and the puppy spherical puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves, the connected curves have 180° rotational symmetry, 90° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves connected head-to-tail divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have the shape characteristics of a puppy.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the puppy.

Preferably, the spherical puzzle is a dancing man spherical puzzle, and the dancing man spherical puzzle is designed based on surface structure characteristics of a regular dodecahedron; regular pentagon surfaces of the regular dodecahedron are each provided with a curve set, the curve sets are rotated by an integer multiple of 72° around centers of the regular pentagon surfaces to form 12 groups of connected curves connected head-to-tail on surfaces of the regular dodecahedron, the connected curves divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, outer contours of the spherical tiles each have shape characteristics of a dancing man, and the spherical puzzle spliced by 12 pieces of the dancing man tiles has 120° rotational symmetry with respect to hands and feet of dancing men.

The resulting technical effect is that the spherical puzzle may be formed by splicing 12 pieces of congruent tiles each having the shape characteristics of the dancing man.

Preferably, the spherical puzzle is a donkey rider spherical puzzle, and the donkey rider spherical puzzle is designed based on surface structure characteristics of a regular octahedron; four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a first type of curve set having 120° rotational symmetry with respect to a center of the surface, other four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a second type of curve set having 120° rotational symmetry with respect to a center of the surface, the first type of curve sets and the second type of curve sets are connected head-to-tail on surfaces of the regular octahedron to form 12 groups of connected curves, the 12 groups of connected curves have 180° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the regular octahedron, and axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, respectively; and the 12 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a donkey rider.

The resulting technical effect is that the spherical puzzle may be formed by splicing 12 pieces of congruent tiles each having the shape characteristics of the donkey rider.

Preferably, the spherical puzzle is a butterfly spherical puzzle, and the butterfly spherical puzzle is designed based on surface structure characteristics of a regular cube; regular quadrilateral surfaces of the regular cube are each provided with a curve set having 90° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular cube to form 24 groups of connected curves, the 24 groups of connected curves have 120° rotational symmetry, 90° rotational symmetry, and 180° rotational symmetry with respect to axes passing through a center and vertexes of the regular cube, axes passing through the center of the regular cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the regular cube and midpoints on sides of the regular quadrilateral surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a butterfly.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the butterfly.

Preferably, the spherical puzzle is a rabbit spherical puzzle, and the rabbit spherical puzzle is designed based on surface structure characteristics of a regular octahedron; four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a first type of curve set having 120° rotational symmetry with respect to a center of the surface, other four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a second type of curve set having 120° rotational symmetry with respect to a center of the surface, the first type of curves set and the second type of curve sets are connected head-to-tail on polygon surfaces of the regular octahedron to form 12 groups of connected curves, the 12 groups of connected curves have 180° rotational symmetry, 120° rotational symmetry and a mirror symmetry with respect to axes passing through a center and vertexes of the regular octahedron, axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, and planes passing through the center of the regular octahedron and sides of the regular triangular surfaces, respectively; and the 12 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a rabbit.

The resulting technical effect is that the spherical puzzle may be formed by splicing 12 pieces of congruent tiles each having the shape characteristics of the rabbit.

Preferably, the spherical puzzle is an octopus spherical puzzle, and the octopus spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 6 groups of connected curves, the connected curves have 180° rotational symmetry, 90° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 6 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 6 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of an octopus.

The resulting technical effect is that the spherical puzzle may be formed by splicing 6 pieces of congruent tiles each having the shape characteristics of the octopus.

Preferably, the spherical puzzle is a lizard spherical puzzle, and the lizard spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on a surface of the truncated cube to form 48 groups of connected curves, the 48 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 48 groups of connected curves divide, after being projected through a center of a sphere, the sphere into two types, 48 pieces of spherical tiles in total, each type of the spherical tiles has 24 congruent pieces in total, and outer contour shapes of the two types of the spherical tiles each have shape characteristics of a lizard.

The resulting technical effect is that the spherical puzzle may be formed by splicing 48 pieces of tiles each having the shape characteristics of two types of the lizard.

Preferably, the spherical puzzle is a cowboy spherical puzzle, and the cowboy spherical puzzle is designed based on surface structure characteristics of a regular dodecahedron; regular pentagon surfaces of the regular dodecahedron are each provided with a curve set, the curve sets are rotated by an integer multiple of 72° around centers of the regular pentagon surfaces to form 12 groups of connected curves connected head-to-tail on surfaces of the regular dodecahedron, the connected curves divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, outer contours of the spherical tiles each have shape characteristic of a cowboy, and the spherical puzzle spliced by 12 pieces of cowboy tiles has a 120° rotational symmetry with respect to elbows and heels of cowboys.

The resulting technical effect is that the spherical puzzle may be formed by splicing 12 pieces of congruent tiles each having the shape characteristics of the cowboy.

Preferably, the spherical puzzle is a strong boy spherical puzzle, and the strong boy spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves, the 24 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a strong boy.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the strong boy.

Preferably, the spherical puzzle is a handsome man spherical puzzle, and the handsome man spherical puzzle is designed based on surface structure characteristics of a regular cube; regular quadrilateral surfaces of the regular cube are each provided with a curve set having 90° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular cube to form 24 groups of connected curves, the 24 groups of connected curves have 120° rotational symmetry, 90° rotational symmetry, and 180° rotational symmetry with respect to axes passing through a center and vertexes of the regular cube, axes passing through the center of the regular cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the regular cube and midpoints on sides of the regular quadrilateral surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a handsome man.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the handsome man.

Preferably, the spherical puzzle is a goat spherical puzzle, and the goat spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves, the 24 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through a center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a goat.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the goat.

Preferably, the spherical puzzle is a frog spherical puzzle, and the frog spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves, the 24 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a frog.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the frog.

Preferably, the spherical puzzle is a singing frog spherical puzzle, and the singing frog spherical puzzle is designed based on surface structure characteristics of a regular octahedron; regular triangular surfaces of the regular octahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular octahedron to form 24 groups of connected curves, the 24 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry, and 120° of rotational symmetry with respect to axes passing through a center of the regular octahedron and midpoints on sides of the regular triangular surfaces, axes passing through the center and vertexes of the regular octahedron, and axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves divide, after being projected through a center of a sphere, the sphere surface into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristic of a singing frog.

The resulting technical effect is that the spherical puzzle may be formed by splicing 24 pieces of congruent tiles each having the shape characteristics of the singing frog.

Preferably, the spherical puzzle is a butterfly spherical puzzle, and the butterfly spherical puzzle is designed based on surface structure characteristics of a regular dodecahedron; regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 60 groups of connected curves, the 60 groups of connected curves have 180° rotational symmetry, 120° rotational symmetry, and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a butterfly.

The resulting technical effect is that the spherical puzzle may be formed by splicing 60 pieces of congruent tiles each having the shape characteristics of the butterfly.

Preferably, the spherical puzzle is a puppy spherical puzzle, and the puppy spherical puzzle is designed based on surface structure characteristics of a regular dodecahedron; regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 60 groups of connected curves, the 60 groups of connected curves have 180° rotational symmetry, 120° rotational symmetry, and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a puppy.

The resulting technical effect is that the spherical puzzle may be formed by splicing 60 pieces of congruent tiles each having the shape characteristics of the puppy.

Preferably, the spherical puzzle is a clown spherical puzzle, and the clown spherical puzzle is designed based on surface structure characteristics of a regular icosahedron; regular triangular surfaces of the regular icosahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular icosahedron to form 60 groups of connected curves, the 60 groups of connected curves have 72° rotational symmetry, 180° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the regular icosahedron, axes passing through the center of the regular icosahedron and midpoints on sides of the regular triangular surfaces, and axes passing through the center of the regular icosahedron and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves connected head-to-tail divided, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have the shape characteristics of a clown.

The resulting technical effect is that the spherical puzzle may be formed by splicing 60 pieces of congruent tiles each having the shape characteristics of the clown.

Preferably, the spherical puzzle is a lizard spherical puzzle, and the lizard spherical puzzle is designed based on surface structure characteristics of a regular icosahedron; regular triangular surfaces of the regular icosahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular icosahedron to form 60 groups of connected curves, the 60 groups of connected curves have 180° rotational symmetry, 72° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center of the regular icosahedron and midpoints on sides of the regular triangular surfaces, axes passing through a center and vertexes of the regular icosahedron, and an axis passing through the center of the regular icosahedron and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a lizard.

The resulting technical effect is that the spherical puzzle may be formed by splicing 60 pieces of congruent tiles each having the shape characteristics of the lizard.

Preferably, the spherical puzzle is a cat spherical puzzle, and the cat spherical puzzle is designed based on surface structure characteristics of a truncated dodecahedron; regular pentagon surfaces of the truncated dodecahedron are each provided with a first curve set having 120° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated dodecahedron are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated dodecahedron to form 60 groups of connected curves, the 60 groups of connected curves have 180° rotational symmetry, 72° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular pentagon surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a cat.

The resulting technical effect is that the spherical puzzle may be formed by splicing 60 pieces of congruent tiles each having the shape characteristics of the cat.

Preferably, the spherical puzzle is a lizard spherical puzzle, and the lizard spherical puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set of 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 72 groups of connected curves, the 72 groups of connected curves have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 72 groups of connected curves divide, after being projected through a center of a sphere, the sphere into three types, 72 pieces of spherical tiles in total, each type of the spherical tiles has 24 congruent pieces in total, and outer contour shapes of the three types of the spherical tiles each have shape characteristics of a lizard.

The resulting technical effect is that the spherical puzzle may be formed by splicing 72 pieces of tiles each having the shape characteristics of three types of the lizard.

Preferably, the spherical puzzle is a platypus spherical puzzle, and the platypus spherical puzzle is designed based on surface structure characteristics of the regular dodecahedron; regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 30 groups of connected curves, the 30 groups of connected curves have 180° rotational symmetry, 120° rotational symmetry and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 30 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 30 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have the shape characteristic of a platypus.

The resulting technical effect is that the spherical puzzle may be formed by splicing 30 pieces of congruent tiles each having the shape characteristics of the platypus.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of Embodiment 1 of the spherical tiling puzzle of the present disclosure;

FIG. 2 is a schematic diagram of Embodiment 2 of the spherical tiling puzzle of the present disclosure;

FIG. 3 is a schematic diagram of Embodiment 3 of the spherical tiling puzzle of the present disclosure;

FIG. 4 is a schematic diagram of Embodiment 4 of the spherical tiling puzzle of the present disclosure;

FIG. 5 is a schematic diagram of Embodiment 5 of the spherical tiling puzzle of the present disclosure;

FIG. 6 is a schematic diagram of Embodiment 6 of the spherical tiling puzzle of the present disclosure;

FIG. 7 is a schematic diagram of Embodiment 7 of the spherical tiling puzzle of the present disclosure;

FIG. 8 is a schematic diagram of Embodiment 8 of the spherical tiling puzzle of the present disclosure;

FIG. 9 is a schematic diagram of Embodiment 9 of the spherical tiling puzzle of the present disclosure;

FIG. 10 is a schematic diagram of Embodiment 10 of the spherical tiling puzzle of the present disclosure;

FIG. 11 is a schematic diagram of Embodiment 11 of the spherical tiling puzzle of the present disclosure;

FIG. 12 is a schematic diagram of Embodiment 12 of the spherical tiling puzzle of the present disclosure;

FIG. 13 is a schematic diagram of Embodiment 13 of the spherical tiling puzzle of the present disclosure;

FIG. 14 is a schematic diagram of Embodiment 14 of the spherical tiling puzzle of the present disclosure;

FIG. 15 is a schematic diagram of Embodiment 15 of the spherical tiling puzzle of the present disclosure;

FIG. 16 is a schematic diagram of Embodiment 16 of the spherical tiling puzzle of the present disclosure;

FIG. 17 is a schematic diagram of Embodiment 17 of the spherical tiling puzzle of the present disclosure;

FIG. 18 is a schematic diagram of Embodiment 18 of the spherical tiling puzzle of the present disclosure;

FIG. 19 is a schematic diagram of Embodiment 19 of the spherical tiling puzzle of the present disclosure;

FIG. 20 is a schematic diagram of Embodiment 20 of the spherical tiling puzzle of the present disclosure;

FIG. 21 is a schematic diagram of Embodiment 21 of the spherical tiling puzzle of the present disclosure;

FIG. 22 is a schematic diagram of Embodiment 22 of the spherical tiling puzzle of the present disclosure;

FIG. 23 is a schematic diagram of Embodiment 23 of the spherical tiling puzzle of the present disclosure;

FIG. 24 is a schematic diagram of Embodiment 24 of the spherical tiling puzzle of the present disclosure;

FIG. 25 is a schematic diagram of Embodiment 25 of the spherical tiling puzzle of the present disclosure;

FIG. 26 is a schematic diagram of Embodiment 26 of the spherical tiling puzzle of the present disclosure;

FIG. 27 is a schematic diagram of Embodiment 27 of the spherical tiling puzzle of the present disclosure;

FIG. 28 is a schematic diagram of Embodiment 28 of the spherical tiling puzzle of the present disclosure;

FIG. 29 is a schematic diagram of Embodiment 29 of the spherical tiling puzzle of the present disclosure;

FIG. 30 is a schematic diagram of Embodiment 30 of the spherical tiling puzzle of the present disclosure;

FIG. 31 is a schematic diagram of Embodiment 31 of the spherical tiling puzzle of the present disclosure;

FIG. 32 is a schematic diagram of Embodiment 32 of the spherical tiling puzzle of the present disclosure;

FIG. 33 is a schematic diagram of Embodiment 33 of the spherical tiling puzzle of the present disclosure;

FIG. 34 is a schematic diagram of Embodiment 34 of the spherical tiling puzzle of the present disclosure;

FIG. 35 is a schematic diagram of Embodiment 35 of the spherical tiling puzzle of the present disclosure;

FIG. 36 is a schematic diagram of Embodiment 36 of the spherical tiling puzzle of the present disclosure;

FIG. 37 is a schematic diagram of Embodiment 37 of the spherical tiling puzzle of the present disclosure;

FIG. 38 is a schematic diagram of Embodiment 38 of the spherical tiling puzzle of the present disclosure;

FIG. 39 is a schematic diagram of Embodiment 39 of the spherical tiling puzzle of the present disclosure;

FIG. 40 is a first schematic diagram of Embodiment 40 of the spherical tiling puzzle of the present disclosure;

FIG. 41 is a second schematic diagram of Embodiment 40 of the spherical tiling puzzle of the present disclosure;

FIG. 42 is a schematic diagram of Embodiment 41 of the spherical tiling puzzle of the present disclosure;

FIG. 43 is an actual product picture of Embodiment 41 of the spherical tiling puzzle of the present disclosure;

FIG. 44 is a first schematic diagram of Embodiment 42 of the spherical tiling puzzle of the present disclosure;

FIG. 45 is a second schematic diagram of Embodiment 42 of the spherical tiling puzzle of the present disclosure;

FIG. 46 is a schematic diagram of Embodiment 43 of the spherical tiling puzzle of the present disclosure;

FIG. 47 is a schematic diagram of Embodiment 44 of the spherical tiling puzzle of the present disclosure;

FIG. 48 is a schematic diagram of Embodiment 45 of the spherical tiling puzzle of the present disclosure;

FIG. 49 is a schematic diagram of Embodiment 46 of the spherical tiling puzzle of the present disclosure;

FIG. 50 is a schematic diagram of Embodiment 47 of the spherical tiling puzzle of the present disclosure;

FIG. 51 is a schematic diagram of Embodiment 48 of the spherical tiling puzzle of the present disclosure;

FIG. 52 is a schematic diagram of Embodiment 49 of the spherical tiling puzzle of the present disclosure;

FIG. 53 is a schematic diagram of Embodiment 50 of the spherical tiling puzzle of the present disclosure;

FIG. 54 is a schematic diagram of Embodiment 51 of the spherical tiling puzzle of the present disclosure;

FIG. 55 is a schematic diagram of Embodiment 52 of the spherical tiling puzzle of the present disclosure;

FIG. 56 is a schematic diagram of Embodiment 53 of the spherical tiling puzzle of the present disclosure;

FIG. 57 is a schematic diagram of Embodiment 54 of the spherical tiling puzzle of the present disclosure;

FIG. 58 is a schematic diagram of Embodiment 55 of the spherical tiling puzzle of the present disclosure;

FIG. 59 is a schematic diagram of Embodiment 56 of the spherical tiling puzzle of the present disclosure; and

FIG. 60 is a schematic diagram of Embodiment 57 of the spherical tiling puzzle of the present disclosure.

• • 1—spherical regular polygon tile; 2—recess; 3—bump; 4—side; and 5—connected curve.

DETAILED DESCRIPTION OF EMBODIMENTS

The following technical solutions in the embodiments of the present disclosure are described clearly and completely in conjunction with the drawings in the embodiments of the present disclosure. It is obvious that the described embodiments are only some, not all of the embodiments of the present disclosure. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without making creative efforts are included in the scope of protection of the present disclosure.

In the present disclosure, FIG. 1-FIG. 37 show combinations of the first series of the present disclosure, and FIG. 38-FIG. 60 show combinations of the second series of the present disclosure.

In the cases of the first series, a puzzle includes a plurality of spherical regular polygon tiles 1. The spherical regular polygon tiles have the same number of sides or different number of sides. The spherical regular polygon tiles are adapted to and engaged with each other through recesses or bumps on sides to form a hollow ball, including two cases. For example, a ball with a regular cube (4.4.4) symmetry may be formed by splicing six pieces of spherical regular quadrilateral tiles each provided with one recess or one bump at a midpoint of the side (see FIG. 19), or by splicing six pieces of the spherical regular quadrilateral tiles each provided with a pair of a recess and a bump having rotational symmetry of 180° with respect to the midpoint of the side (see FIG. 2).

The first series includes 5 regular polyhedrons and 13 Archimedean solids, divided into two cases.

In a first case, sides of the spherical regular polygon tiles are each provided with a group of a recess 2 and a bump 3 having rotational symmetry of 180° with respect to the midpoint of the side. In the splicing, the sides of the spherical regular polygon tiles are aligned, the recesses 2 and the bumps 3 provided on the sides of the tiles are precisely aligned and engaged with each other to be spliced into a ball. Reference may be made to FIG. 1-FIG. 18 for presentation.

When the sides of the spherical regular polygon tiles are each provided with both a first connecting structure and a second connecting structure, the first connecting structure and the second connecting structure form the rotational symmetry of 180° with respect to the midpoint of the side. In addition, the side provided with the first connecting structure and the second connecting structure has rotational symmetry with respect to a center of the spherical regular polygon tiles. This design ensures the engagement universality of the joints of the spherical regular polygon tiles.

In a second case, the sides of the spherical regular polygon tiles are each provided with only one connecting structure at the midpoint of the side, and the connecting structure may be in the shape of the recess 2 or the bump 3. In the splicing, the sides of the spherical regular polygon tiles are aligned, the recess 2 and the bump 3 provided on the sides of adjacent tiles are precisely aligned and engaged with each other to be spliced into a ball, referring to FIG. 19-FIG. 37. Specifically, in the process of splicing, two spherical regular polygon tiles provided with the first connecting structure (recesses 2) and the second connecting structure (bumps 3) at the midpoints of the sides respectively are adapted to, and aligned and engaged with each other along the sides. It is necessary to be clear that the total number of the recesses 2 of the spherical regular polygon tiles used must be equal to the total number of the bumps 3, ensuring that the recesses and bumps of the polygon tiles are paired and engaged to form a stable structure.

In the process of splicing, the types, numbers and combinations of the spherical regular polygon tiles used are in one-to-one correspondence with the types, numbers and combinations of regular polygons of 5 regular polyhedrons or 13 Archimedean solids. It is to be understood that the regular polygon surfaces of the 5 regular polyhedrons or the 13 Archimedean solids are replaced with spherical regular polygon tiles provided with proper connecting structures on the sides, and then the corresponding spherical puzzle may be obtained splicing.

Referring to FIG. 1, Embodiment 1 shows a spherical puzzle (3.3.3) constructed by 4 pieces of spherical regular triangular tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 2, Embodiment 2 shows the spherical puzzle (4.4.4) constructed by 6 pieces of spherical regular quadrilateral tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 3, Embodiment 3 shows the spherical puzzle (3.3.3.3) constructed by 8 pieces of spherical regular triangular tiles, and the difference with Embodiment 1 is an increase in the number of the spherical regular triangular tiles.

Referring to FIG. 4, Embodiment 4 shows the spherical puzzle (5.5.5) constructed by 12 pieces of spherical regular pentagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 5, Embodiment 5 shows the spherical puzzle (3.3.3.3.3) constructed by 20 pieces of spherical regular triangular tiles, and the difference with Embodiment 3 is an increase in the number of the spherical regular triangular tiles.

Referring to FIG. 6, Embodiment 6 shows the spherical puzzle (3.4.3.4) constructed by combining 8 pieces of spherical regular triangular tiles and 6 pieces of the spherical regular quadrilateral tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 7, Embodiment 7 shows the spherical puzzle (3.5.3.5) constructed by combining 20 pieces of spherical regular triangular tiles and 12 pieces of spherical regular pentagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 8, Embodiment 8 shows the spherical puzzle (3.6.6) constructed by combining 4 pieces of spherical regular triangular tiles and 4 pieces of spherical regular hexagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 9, Embodiment 9 shows the spherical puzzle (3.8.8) constructed by combining 8 pieces of spherical regular triangular tiles and 6 pieces of spherical regular octagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 10, Embodiment 10 shows the spherical puzzle (4.6.6) constructed by combining 6 pieces of spherical regular quadrilateral tiles and 8 pieces of spherical regular hexagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 11, Embodiment 11 shows the spherical puzzle (3.4.4.4) constructed by combining 8 pieces of spherical regular triangular tiles and 18 pieces of spherical regular quadrilateral tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 12, Embodiment 12 shows the spherical puzzle (4.6.8) constructed by combining 12 pieces of spherical regular triangular tiles, 8 pieces of spherical regular hexagon tiles and 6 pieces of spherical regular octagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 13, Embodiment 13 shows the spherical puzzle (3.3.3.3.4) constructed by combining 32 pieces of spherical regular triangular tiles and 6 pieces of spherical regular quadrilateral tiles, the sides of the spherical regular polygon tiles are provided with recess and bump structures, and the splicing combination is different from those of Embodiment 6 and Embodiment 11.

Referring to FIG. 14, Embodiment 14 shows the spherical puzzle (5.6.6) constructed by combining 12 pieces of spherical regular pentagon tiles and 20 pieces of spherical regular hexagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 15, Embodiment 15 shows the spherical puzzle (3.4.5.4) constructed by combining 20 pieces of spherical regular triangular tiles, 30 pieces of spherical regular quadrilateral tiles and 12 pieces of spherical regular pentagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 16, Embodiment 16 shows the spherical puzzle (3.3.3.3.5) constructed by combining 80 pieces of spherical regular triangular tiles and 12 pieces of spherical regular pentagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 17, Embodiment 17 shows the spherical puzzle (4.6.10) constructed by combining 30 pieces of spherical regular quadrilateral tiles, 20 pieces of spherical regular hexagon tiles and 12 pieces of spherical regular decagon tiles, and the sides of the tiles are provided with recess and bump structures.

Referring to FIG. 18, Embodiment 18 shows the spherical puzzle (3.10.10) constructed by combining 20 pieces of spherical regular triangular tiles and 12 pieces of spherical regular decagon tiles, and the sides of the tiles are provided with recess and bump structures.

Embodiments 1-18 have common features that each side of the spherical regular polygon tile is provided with two connecting structures (recess and bump), and the two connecting structures (recess and bump) have the rotational symmetry of 180° with respect to the midpoint of the corresponding side.

Referring to FIG. 19, Embodiment 19 shows the spherical puzzle (4.4.4) formed by splicing 6 pieces of congruent spherical regular quadrilateral tiles, and a midpoint of a side of a tile is provided with a notch or bump structure.

Referring to FIG. 20, Embodiment 20 shows the spherical puzzle (4.6.6) constructed by combining 6 pieces of spherical regular quadrilateral tiles and 8 pieces of spherical regular hexagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 21, Embodiment 21 shows the spherical puzzle (4.6.8) constructed by combining 12 pieces of spherical regular quadrilateral tiles, 8 pieces of spherical regular hexagon tiles and 6 pieces of spherical regular octagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 22, Embodiment 22 shows the spherical puzzle (4.6.10) constructed by combining 30 pieces of spherical regular quadrilateral tiles, 20 pieces of spherical regular hexagon tiles and 12 pieces of spherical regular decagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 23, Embodiment 23 shows the spherical puzzle (3.8.8) constructed by combining 8 pieces of spherical regular triangular tile and 6 pieces of spherical regular octagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 24, Embodiment 24 shows the spherical puzzle (3.4.5.4) constructed by combining 20 pieces of spherical regular triangular tiles, 30 pieces of spherical regular quadrilateral tiles and 12 pieces of spherical regular pentagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 25, Embodiment 25 shows the spherical puzzle (3.4.3.4) constructed by combining 8 pieces of spherical regular triangular tiles and 6 pieces of spherical regular quadrilateral tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 26, Embodiment 26 shows the spherical puzzle (3.5.3.5) constructed by combining 20 pieces of spherical regular triangular tiles and 30 pieces of spherical regular pentagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 27, Embodiment 27 shows the spherical puzzle (5.6.6) constructed by combining 12 pieces of spherical regular pentagon tiles and 20 pieces of spherical regular hexagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 28, Embodiment 28 shows also the spherical puzzle (5.6.6) constructed by combining 12 pieces of spherical regular pentagon tiles and 20 pieces of spherical regular hexagon tiles, and the midpoint of the side of the spherical regular polygon tile is provided with only one recess or bump. Compared to Embodiment 27, the layout of the connecting structures on the sides of the spherical regular polygon tiles is different.

Referring to FIG. 29, Embodiment 29 shows the spherical puzzle (3.3.3.3.4) constructed by combining 32 pieces of spherical regular tiles and 6 pieces of spherical regular quadrilateral tiles, and the midpoint of the side of the spherical regular polygon tile is provided with only one recess or bump. Compared to Embodiment 13, the layout of spliced connection structures is different.

Referring to FIG. 30, Embodiment 30 shows the spherical puzzle (3.3.3.3) constructed by 8 pieces of spherical regular triangular tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 31, Embodiment 31 shows the spherical puzzle (5.5.5) constructed by 12 pieces of spherical regular pentagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 32, Embodiment 32 shows the spherical puzzle (3.3.3.3.3) constructed by 20 pieces of spherical regular triangular tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 33, Embodiment 33 shows the spherical puzzle (3.6.6) constructed by 4 pieces of spherical regular triangular tiles and 4 pieces of spherical regular hexagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 34, Embodiment 34 shows the spherical puzzle (3.4.4.4) constructed by 8 pieces of spherical regular triangular tiles and 18 pieces of spherical regular quadrilateral tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 35, Embodiment 35 shows the spherical puzzle (3.3.3.3.4) constructed by 32 pieces spherical regular triangular tiles and 6 pieces of spherical regular quadrilateral tile, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 36, Embodiment 36 shows the spherical puzzle (3.10.10) constructed by 20 pieces of spherical regular triangular tiles and 12 pieces of spherical regular decagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Referring to FIG. 37, Embodiment 37 shows the spherical puzzle (3.3.3.3.5) constructed by 80 pieces of spherical regular triangular tiles and 12 pieces of spherical regular pentagon tiles, and the midpoint of the side of the tile is provided with a recess or bump structure.

Embodiments 19-37 have common features that only one connecting structure (recess or bump) is provided at the midpoint of the side of the spherical regular polygon tile in the spherical puzzle, and the total number of the recesses and the total number of the bumps in the spherical puzzle are equal.

It should be illustrated that for the foregoing embodiments, the first connecting structure and the second connecting structure are not limited to the recess and the bump, but may also be other structures that may be engaged with each other.

It should be illustrated that for the foregoing embodiments, under the central projection correspondence, the types, numbers and combinations of spherical regular polygon tiles in the spherical puzzles of the first series correspond one by one to those of 5 regular polyhedrons or 13 Archimedean solids, respectively. Therefore, the sides of all spherical regular polygon tiles are equal in length.

Embodiment 38 shows a puppy spherical puzzle. Referring to FIG. 38, the puzzle is designed based on surface structure characteristics of a truncated cube; regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curves have 180° rotational symmetry with respect to vertexes of the truncated cube respectively, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves 5, the 24 groups of connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the connected curves connected head-to-tail divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a puppy.

Embodiment 39 shows a dancing man puppy spherical puzzle. Referring to FIG. 39, the puzzle is designed based on surface structure characteristics of a regular dodecahedron, and 12 regular pentagon surfaces of the regular dodecahedron are provided with same curve sets. After the curve sets of the regular pentagons are rotated by an integer multiple of 72° along centers, the connected curves connected head-to-tail are formed, referring to FIG. 39. In FIG. 39, while a curve on a side CD is rotated 120° around a point C to a side CB, the curve on a side AB is rotated 120° around a point A to a side AE. The curves on a spherical regular pentagon ABCDE and five adjacent spherical regular pentagons thereof just form 12 groups of congruent connected curves 5 that are connected head-to-tail. After the connecting curves 5 divide, after being projected through a center of a sphere, the sphere into 12 spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a dancing man. A ball spliced by 12 tiles each having characteristic of a dancing man has 120° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and intersections of three hands, and axes passing through the center of the regular dodecahedron and intersections of three feet.

Embodiment 40 shows a donkey rider spherical puzzle. Referring to FIG. 40-FIG. 41, the puzzle is designed based on surface structure characteristics of a regular octahedron; four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a first type of curve set having 120° rotational symmetry with respect to a center of the surface, other four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a second type of curve set having 120° rotational symmetry with respect to a center of the surface, the first type of curve sets and the second type of curve sets are connected head-to-tail on surfaces of the regular octahedron to form 12 groups of connected curves 5, the 12 groups of connected curves 5 have 180° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the regular octahedron and axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, respectively; and the 12 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a donkey rider.

Embodiment 41 shows a butterfly spherical puzzle. Referring to FIG. 42, the puzzle is designed based on surface structure characteristics of a regular cube; regular quadrilateral surfaces of the regular cube are each provided with a curve set having 90° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular cube to form 24 groups of connected curves 5, the 24 groups of connected curves have 120° rotational symmetry, 90° rotational symmetry and 180° rotational symmetry with respect to axes passing through a center and vertexes of the regular cube, axes passing through the center of the regular cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the regular cube and midpoints on sides of the regular quadrilateral surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a butterfly.

Reference is made to FIG. 43 which shows an actual product state of Embodiment 41.

Embodiment 42 shows a rabbit spherical puzzle. Referring to FIG. 44-FIG. 45, the puzzle is designed based on surface structure characteristics of a regular octahedron; four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a first type of curve set having 120° rotational symmetry with respect to a center of the surface, other four non-adjacent regular triangular surfaces of the regular octahedron are each provided with a second type of curve set having 120° rotational symmetry with respect to a center of the surface, the first type of curve sets and the second type of curve sets are connected head-to-tail on polygon surfaces of the regular octahedron to form 12 groups of connected curves 5, the 12 groups of connected curves 5 have 180° rotational symmetry, 120° rotational symmetry and a mirror symmetry with respect to axes passing through a center and vertexes of the regular octahedron, axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, and planes passing through the center of the regular octahedron and sides of the regular triangular surfaces, respectively; and the 12 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have the shape characteristics of a rabbit.

Embodiment 43 shows an octopus spherical puzzle. Referring to FIG. 46, the puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 6 groups of connected curves 5, the 6 groups of connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 6 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 6 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have the shape characteristics of an octopus.

Embodiment 44 shows a lizard spherical puzzle. Referring to FIG. 47, the puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, and regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface. The first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 48 groups of connected curves 5, the 48 groups of connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 48 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into two different types of spherical tiles, each type of the spherical tiles has 24 congruent pieces, and outer contour shapes of the two types of spherical tiles each have shape characteristics of a lizard.

Embodiment 45 shows a cowboy spherical puzzle. Referring to FIG. 48, the puzzle is designed based on surface structure characteristics of a regular dodecahedron. Regular pentagon surfaces of the regular dodecahedron are provided with a curve set, the curve sets are rotated by an integer multiple of 72° around centers of the regular pentagon surfaces to form 12 groups of connected curves 5 connected head-to-tail on surfaces of the regular dodecahedron, the connected curves 5 divide, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, outer contours of the spherical tiles each have the shape characteristic of a cowboy, and a ball spliced by 12 tiles having characteristics of the cowboy has a 120° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and intersections of three elbows, and axes passing through the center of the regular dodecahedron and intersections of three heels.

Embodiment 46 shows a strong boy spherical puzzle. Referring to FIG. 49, the puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 24 groups of connected curves 5, the connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and the spherical tiles each have outer contour characteristics of a human portrait.

Embodiment 47 shows a handsome man spherical puzzle. Referring to FIG. 50, the puzzle is designed based on surface structure characteristics of a regular cube, regular quadrilateral surfaces of the regular cube are each provided with a curve set having 90° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on polygon surfaces of the regular cube to form 24 groups of connected curves 5, the 24 groups of connected curves 5 have 120° rotational symmetry, 90° rotational symmetry, and 180° rotational symmetry with respect to axes passing through a center and vertexes of the regular cube, axes passing through the center of the regular cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the regular cube and midpoints on sides of the regular quadrilateral surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and the spherical tiles each have shape outer contour characteristics of a human portrait.

Embodiment 48 shows a goat spherical puzzle. Referring to FIG. 51, the puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 24 groups of connected curves 5, the connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles have shape characteristics of a strong goat.

Embodiment 49 is a frog spherical puzzle. Referring to FIG. 52, the puzzle is designed based on surface structure characteristics of a truncated cube. Regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on polygon surfaces of the truncated cube to form 24 groups of connected curves 5, the connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles have shape characteristics of a frog.

Embodiment 50 shows a singing frog spherical puzzle. Referring to FIG. 53, the puzzle is designed based on surface structure characteristics of a regular octahedron, regular triangular surfaces of a regular octahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular octahedron to form 24 groups of connected curves 5, the 24 groups of connected curves 5 have 180° rotational symmetry, 90° rotational symmetry and 120° rotational symmetry with respect to axes passing through a center of the regular octahedron and midpoints on sides of the regular triangular surfaces, axes passing through a center and vertexes of the regular octahedron, and axes passing through the center of the regular octahedron and centers of the regular triangular surfaces, respectively; and the 24 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles have shape characteristics of a singing frog.

Embodiment 51 shows a butterfly spherical puzzle. Referring to FIG. 54, the puzzle is designed based on surface structure characteristics of a regular dodecahedron, regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 72° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 60 groups of connected curves 5, the 60 groups of connected curves have 180° rotational symmetry, 120° rotational symmetry and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 60 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles have shape characteristics of a butterfly.

Embodiment 52 shows a puppy spherical puzzle. Referring to FIG. 55, the puzzle is designed based on surface structure characteristics of a regular dodecahedron, regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 72° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 60 groups of connected curves 5, the 60 groups of connected curves 5 have 180° rotational symmetry, 120° rotational symmetry and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a puppy.

Embodiment 53 shows a clown spherical puzzle. Referring to FIG. 56, the puzzle is designed based on surface structure characteristics of a regular icosahedron, regular triangular surfaces of the regular icosahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular icosahedron to form 60 groups of connected curves 5, the 60 groups of connected curves 5 have 180° rotational symmetry, 72° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center of the regular icosahedron and midpoints on sides of the regular triangular surfaces, axes passing through the center and vertexes of the regular icosahedron surfaces, and axes passing through the center of the regular triangular and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves 5 divide, after being projected by a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a clown.

Embodiment 54 shows a lizard spherical puzzle. Referring to FIG. 57, the puzzle is designed based on surface structure characteristics of a regular icosahedron, regular triangular surfaces of the regular icosahedron are each provided with a curve set having 120° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular icosahedron to form 60 groups of connected curves 5, the 60 groups of connected curves 5 have 180° rotational symmetry, 72° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center of the regular icosahedron and midpoints on sides of the regular triangular surfaces, axes passing through the center and vertexes of the regular icosahedron surfaces, and axes passing through the center of the regular icosahedron and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves divide, after being projected through a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a lizard.

Embodiment 55 shows a cat spherical puzzle. Referring to FIG. 58, the puzzle is designed based on surface structure characteristics of a truncated dodecahedron, regular pentagon surfaces of the truncated dodecahedron are each provided with a first curve set having 72° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated dodecahedron are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated dodecahedron to form 60 groups of connected curves 5, the 60 groups of connected curves have 180° rotational symmetry, 72° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated dodecahedron, axes passing through the center of the truncated dodecahedron and centers of the regular pentagon surfaces, and axes passing through the center of the truncated dodecahedron and centers of the regular triangular surfaces, respectively; and the 60 groups of connected curves 5 divide, after being projected by a center of a sphere, the sphere into 60 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a cat.

Embodiment 56 shows a lizard spherical puzzle. Referring to FIG. 59, the puzzle is designed based on surface structure characteristics of a truncated cube, regular quadrilateral surfaces of the truncated cube are each provided with a first curve set having 90° rotational symmetry with respect to a center of the surface, regular triangular surfaces of the truncated cube are each provided with a second curve set having 120° rotational symmetry with respect to a center of the surface, the first curve sets and the second curve sets are connected head-to-tail on surfaces of the truncated cube to form 72 groups of connected curves 5, the connected curves 5 have 180° rotational symmetry, 90° rotational symmetry, and 120° rotational symmetry with respect to axes passing through a center and vertexes of the truncated cube, axes passing through the center of the truncated cube and centers of the regular quadrilateral surfaces, and axes passing through the center of the truncated cube and centers of the regular triangular surfaces, respectively; and the 72 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into three different types of spherical tiles, each type of the spherical tiles has 24 congruent pieces, and the three types of spherical tiles each have outer contour characteristic of a lizard.

Embodiment 57 shows a platypus spherical puzzle. Referring to FIG. 60, the puzzle is designed based on surface structure characteristics of a regular dodecahedron, regular pentagon surfaces of the regular dodecahedron are each provided with a curve set having 72° rotational symmetry with respect to a center of the surface, the curve sets are connected head-to-tail on surfaces of the regular dodecahedron to form 30 groups of connected curves 5, the connected curves have 180° rotational symmetry, 120° rotational symmetry, and 72° rotational symmetry with respect to axes passing through a center of the regular dodecahedron and midpoints on sides of the regular pentagon surfaces, axes passing through the center and vertexes of the regular dodecahedron, and axes passing through the center of the regular dodecahedron and centers of the regular pentagon surfaces, respectively; and the 30 groups of connected curves 5 divide, after being projected through a center of a sphere, the sphere into 30 pieces of congruent spherical tiles, and the spherical tiles each have outer contour characteristic of a platypus.

The symmetrical structure of the spherical puzzle constructed in the present disclosure is based on 5 regular polyhedrons or 13 Archimedean solids, totaling two series. The first series of the spherical puzzle is divided into two types, 37 implementation examples in total, and the second series of the spherical puzzle has a total of 20 implementation examples. The summary is as follows.

The first series of the spherical puzzle has two kinds, and a puzzle structure corresponds to 5 regular polyhedrons and 13 Archimedean solids. For the first kind, each side of the spherical regular polygon tile of the spherical puzzle is provided with a group of bump and recess, the bump and recess are of the same shape and size, and the bump and recess form the rotational symmetry of 180° with respect to the midpoint of the side. In addition, the side provided with the bump and the recess has rotational symmetry with respect to the center of the spherical regular polygon tile. For the second kind, the side of the spherical regular polygon tile on the spherical puzzle is provided on the midpoint thereof with either a single recess, or a single bump, so as to ensure that the spherical regular polygon tiles are adapted to and engaged with each other on the sides during splicing, and the total numbers of the bumps and the recesses on the spherical puzzle are equal.

The tiles of the second series of the spherical puzzle each have the contour appearance of a human portrait or an animal, because they are designed according to the symmetry principle of regular polyhedron or Archimedean solids. Therefore, the human portrait or animal tiles on the spherical puzzle forms a rotational symmetry or mirror symmetry at a specific angle with respect to axes passing through the center and vertexes of the polyhedron, axes passing through the center of the polyhedron and the centers of the regular polygon surfaces, axes passing through the center of the polyhedron and the midpoints of the sides of the regular polygon surfaces, and planes passing through the midpoint of the polyhedron and the sides of the regular polygon surfaces. The main properties of them are summarized in Table 1.

For devices and use methods disclosed in the embodiments, the description is relatively simple because they correspond to methods disclosed in the embodiments, and reference may be made to the method sections for relevant parts.

The foregoing description of the disclosed embodiments enables those of ordinary skill in the art to realize or use the present disclosure. Various modifications to these embodiments are obvious to those of ordinary skill in the art, and the general principles defined herein may be achieved in other examples without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure is not to be limited to the embodiments shown herein, but is to be conformed to the widest scope consistent with the principles and novel features disclosed herein.