Regular Polyhedron Generator

This is a generator that helps you create various regular polyhedra, including Platonic solids, Archimedean solids, and Catalan solids.

1、Platonic solids：is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra.

Polyhedron		Vertices	Edges	Faces	Schläfli symbol	Vertex configuration
Regular tetrahedron		4	6	4	{3, 3}	3.3.3
cube		8	12	6	{4, 3}	4.4.4
Regular octahedron		6	12	8	{3, 4}	3.3.3.3
Regular dodecahedron		20	30	12	{5, 3}	5.5.5
Regular icosahedron		12	30	20	{3, 5}	3.3.3.3.3

2、Archimedean solids：are a set of thirteen convex polyhedra whose faces are regular polygons and are vertex-transitive, although they are not face-transitive.

Name	Solids	Vertex configurations	Faces	Edges	Vertices
Truncated tetrahedron		3.6.6	4 triangles 4 hexagons	18	12
Cuboctahedron		3.4.3.4	8 triangles 6 squares	24	12
Truncated cube		3.8.8	8 triangles 6 octagons	36	24
Truncated octahedron		4.6.6	6 squares 8 hexagons	36	24
Rhombicuboctahedron		3.4.4.4	8 triangles 18 squares	48	24
Truncated cuboctahedron		4.6.8	12 squares 8 hexagons 6 octagons	72	48
Snub cube		3.3.3.3.4	32 triangles 6 squares	60	24
Icosidodecahedron		3.5.3.5	20 triangles 12 pentagons	60	30
Truncated dodecahedron		3.10.10	20 triangles 12 decagons	90	60
Truncated icosahedron		5.6.6	12 pentagons 20 hexagons	90	60
Rhombicosidodecahedron		3.4.5.4	20 triangles 30 squares 12 pentagons	120	60
Truncated icosidodecahedron		4.6.10	30 squares 20 hexagons 12 decagons	180	120
Snub dodecahedron		3.3.3.3.5	80 triangles 12 pentagons	150	60

3、Catalan solids：are the dual polyhedra of Archimedean solids. The Archimedean solids are thirteen highly-symmetric polyhedra with regular faces and symmetric vertices.The faces of the Catalan solids correspond by duality to the vertices of Archimedean solids, and vice versa.

Name	Image	Faces	Edges	Vertices	Dihedral angle
triakis tetrahedron		12 isosceles triangles	18	8	129.521°
rhombic dodecahedron		12 rhombi	24	14	120°
triakis octahedron		24 isosceles triangles	36	14	147.350°
tetrakis hexahedron		24 isosceles triangles	36	14	143.130°
deltoidal icositetrahedron		24 kites	48	26	138.118°
disdyakis dodecahedron		48 scalene triangles	72	26	155.082°
pentagonal icositetrahedron		24 pentagons	60	38	136.309°
rhombic triacontahedron		30 rhombi	60	32	144°
triakis icosahedron		60 isosceles triangles	90	32	160.613°
pentakis dodecahedron		60 isosceles triangles	90	32	156.719°
deltoidal hexecontahedron		60 kites	120	62	154.121°
disdyakis triacontahedron		120 scalene triangles	180	62	164.888°
pentagonal hexecontahedron		60 pentagons	150	92	153.179°

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