List of convex regular-faced polyhedra (Meta, 13)
From Hi.gher. Space
Three classes used in the table below:
- B = Brick: point (x, y, z) implies point (±x, ±y, ±z)
- S = Simple: exactly three faces meet at each vertex
- Z = Zonotope: each face has point symmetry
| Index | Parent | Elements | Dual | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Name | Classes | SSC2 | Faces | Edges | Vertices | Name | Classes | SSC2 | |
| Platonic solids (total 5) | |||||||||
| 1 | Tetrahedron | -S- | Kt1 | 4 | 6 | 4 | Self-dual | ||
| 2 | Cube | BSZ | Ko1 | 6 | 12 | 8 | 3. Octahedron (below) | ||
| 3 | Octahedron | B-- | Ko4 | 8 | 12 | 6 | 2. Cube (above) | ||
| 4 | Dodecahedron | BS- | Ki1 | 12 | 30 | 20 | 5. Icosahedron (below) | ||
| 5 | Icosahedron | B-- | Ki4 | 20 | 30 | 12 | 4. Dodecahedron (above) | ||
| Archimedean solids (total 13) | |||||||||
| 6 | Tetrahedral truncate | -S- | Kt3 | 8 | 18 | 12 | Triakis tetrahedron | --- | Unknown |
| 7 | Cuboctahedron | B-- | Ko2 | 14 | 24 | 12 | Rhombic dodecahedron | B-Z | Unknown |
| 8 | Cubic truncate | BS- | Ko3 | 14 | 36 | 24 | Triakis octahedron | B-- | Unknown |
| 9 | Octahedral truncate | BS- | Ko6 | 14 | 36 | 24 | Tetrakis hexahedron | B-- | Unknown |
| 10 | Cuboctahedral rectate | B-- | Ko5 | 26 | 48 | 24 | Deltoidal icositetrahedron | --- | Unknown |
| 11 | Cuboctahedral truncate | BSZ | Ko7 | 26 | 72 | 48 | Disdyakis dodecahedron | B-- | Unknown |
| 12 | Cubic snub | --- | Ko0 | 38 | 60 | 24 | Pentagonal icositetrahedron | --- | Unknown |
| Utility prisms (total 9) | |||||||||
| Johnson solids (total 92) | |||||||||
