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Descrição
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° |
