Spherical tiling puzzle

Abstract

Disclosed is a spherical tiling puzzle which is formed by combining a plurality of spherical tiles. The spherical tiles are each provided with a spherical regular polygon as a basic design element. The plurality of 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 hollow spherical puzzle according to surface layouts of five regular polyhedrons or thirteen Archimedean 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.

1 . A spherical tiling puzzle, comprising a plurality of spherical tiles, wherein the spherical tiles are each provided with a spherical regular polygon as a basic design element, the plurality of 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 which is hollow according to surface layouts of five regular polyhedrons or thirteen Archimedean solids, and the spherical tiles provided through deformation of the spherical regular polygons as the basic design elements have various outer contour shapes. 
     
     
         2 . The spherical tiling puzzle according to  claim 1 , wherein when the outer contour shapes of the plurality of spherical tiles constituting the spherical puzzle are polygon-like shapes, each side of any of the spherical tiles is 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 of first connecting structures are adapted to and spliced with outer contour shapes of the second connecting structures, the plurality of spherical tiles are spliced into the spherical puzzle through mutual engagement of the first connecting structures and the second connecting structures, the first connecting structures and the second connecting structures on sides of the plurality of spherical regular polygons constituting the spherical puzzle have same total numbers, and sides of the plurality of spherical regular polygon tiles constituting the spherical puzzle are equal in length. 
     
     
         3 . The spherical tiling puzzle according to  claim 2 , wherein when the each side of the plurality of spherical tiles constituting the spherical puzzle is provided with one connecting structure, the first connecting structure or the second connecting structure on the side of any of the spherical regular polygon tiles is positioned at a midpoint of the side, and the first connecting structure on the side of any of the spherical regular polygon tiles is adapted to and spliced with the second connecting structure on the side of a spherical regular polygon tile adjacent thereto. 
     
     
         4 . The spherical tiling puzzle according to  claim 2 , wherein when the each side of the plurality of spherical tiles constituting the spherical puzzle are provided with a plurality of connecting structures, the first connecting structure and the second connecting structure on the side of any of the spherical regular polygon tiles have rotational symmetry with respect to a midpoint of the side, and the side of any of the spherical regular polygon tiles has rotational symmetry with respect to a center of the spherical tile. 
     
     
         5 . The spherical tiling puzzle according to  claim 1 , wherein the spherical puzzle is a puppy spherical puzzle,
 wherein 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 surface 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 shape characteristics of a puppy; or   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 the puppy.   
     
     
         6 . The spherical tiling puzzle according to  claim 1 , wherein 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 a surface of the regular dodecahedron, 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, 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 the dancing men. 
     
     
         7 . The spherical tiling puzzle according to  claim 1 , wherein 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 a surface 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 divides, after being projected through a center of a sphere, the sphere into 12 pieces of congruent spherical tiles, and the outer contours of the spherical tiles each have shape characteristics of a donkey rider. 
     
     
         8 . The spherical tiling puzzle according to  claim 1 , wherein the spherical puzzle is a butterfly spherical puzzle,
 wherein 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; or   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 the butterfly.   
     
     
         9 . The spherical tiling puzzle according to  claim 1 , wherein 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 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, 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. 
     
     
         10 . The spherical tiling puzzle according to  claim 1 , wherein 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. 
     
     
         11 . The spherical tiling puzzle according to  claim 1 , wherein the spherical puzzle is a lizard spherical puzzle,
 wherein 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 surfaces 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; or   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 the center and vertexes of the regular icosahedron 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 the lizard; or   the lizard spherical puzzle is designed based on surface structure characteristics of the 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, 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 spherical tiles each have shape characteristic of a lizard.   
     
     
         12 . The spherical tiling puzzle according to  claim 1 , wherein 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 a surface of the regular dodecahedron, 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, outer contours of the spherical tiles each have shape characteristic of a cowboy, and the spherical puzzle spliced by 12 pieces of the cowboy tiles has a 120° rotational symmetry with respect to elbows and heels of cowboys. 
     
     
         13 . The spherical tiling puzzle according to  claim 1 , wherein 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. 
     
     
         14 . The spherical tiling puzzle according to  claim 1 , wherein 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. 
     
     
         15 . The spherical tiling puzzle according to  claim 1 , wherein 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 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 goat. 
     
     
         16 . The spherical tiling puzzle according to  claim 1 , wherein 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. 
     
     
         17 . The spherical tiling puzzle according to  claim 1 , wherein 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° 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 into 24 pieces of congruent spherical tiles, and outer contours of the spherical tiles each have shape characteristics of a singing frog. 
     
     
         18 . The spherical tiling puzzle according to  claim 1 , wherein 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 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 clown. 
     
     
         19 . The spherical tiling puzzle according to  claim 1 , wherein 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 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 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. 
     
     
         20 . The spherical tiling puzzle according to  claim 1 , wherein the spherical puzzle is a platypus spherical puzzle, and the platypus 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 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 shape characteristic of a platypus.