Icosadodecahedron puzzle system

Abstract

The IKOS holistic game of this invention comprises a semi-regular geometric solid of 32 faces. 12 faces are regular pentagons interfaced to 20 equilateral triangles. The polyhedron also comprises 60 equal upstand edges each one of which subtends 36 degrees at the centroid of the polyhedron. It also comprises 30 equal vertices at which four edges and four faces meet. The surface elements 1 of the IKOS are of seven distinct colors, with each surface element being of one color only. There are six sets of like colored surface elements with two pentagons and ten up-stands in each set. All the triangular panels are in the seventh, neutral, shade. Also included is a method of designing the 32'dron on a CAD system.

The inventor claims:  
     
         1 . An icosadodecahedron puzzle system comprising 12 pentagons symmetrically and geometrically and rotationally interfaced to 20 equilateral triangles and 60 upstand edges resulting in two hemispheres each with plurality of pentagonal florets and triangular florets.  
     
     
         2 . The icosadodecahedron puzzle system of  claim 1  wherein; 
 a) said pentagons are regular and identical shape; and  
 b) said 60 upstand edges are all equal.  
 
     
     
         3 . The icosadodecahedron puzzle system of  claim 1  wherein; 
 a) each one of said edges subtends 30 degrees at the centroid of said icosadodecahedron; and  
 b) said icosadodecahedron further having 30 equal vertices.  
 
     
     
         4 . The icosadodecahedron puzzle system of  claim 3  wherein at each of said 30 equal vertices 4 of said 60 equal edges and four of said 32 faces meet.  
     
     
         5 . An polyhedron puzzle system comprising 12 pentagons symmetrically and geometrically and rotationally interfaced to 20 equilateral triangles and 60 upstand edges resulting in two hemispheres each with plurality of pentagonal florets and triangular florets.  
     
     
         6 . The polyhedron puzzle system of  claim 5  which is an icosadodecahedron puzzle with 32 sides.  
     
     
         7 . The polyhedron puzzle system of  claim 6  wherein; 
 a) said pentagons are regular and identical shape; and  
 b) said 60 upstand edges are all equal.  
 
     
     
         8 . The polyhedron puzzle system of  claim 7  wherein; 
 a) each one of said edges subtends 30 degrees at the centroid of said icosadodecahedron; and  
 b) said icosadodecahedron further has 30 equal vertices.  
 
     
     
         9 . The polyhedron puzzle system of  claim 8  wherein at each of said 30 equal vertices four of said 60 equal edges meet.  
     
     
         10 . The polyhedron puzzle system of  claim 8  wherein at each of said 30 equal vertices four of said 32 faces meet.  
     
     
         11 . A polyhedron of 32 faces of 12 regular pentagons and 20 equilateral triangles having 60 equal edges rotationally interconnected symmetrically and geometrically resulting in two hemispheres each with plurality of pentagonal florets and triangular florets wherein each one of said edges subtends 30 degrees at the centroid of said polyhedron and said polyhedron further having 30 equal vertices wherein at each of said 30 equal vertices 4 of said 60 equal edges and four of said 32 faces meet.