See main article: Icosahedral symmetry.
Platonic solids - regular polyhedra (all faces of the same type)
Archimedean solids - polyhedra with more than one polygon face type.
| 50px 3.10.10 | 50px 4.6.10 | 50px 5.6.6 | 50px 3.4.5.4 | 50px 3.5.3.5 |
Catalan solids - duals of the Archimedean solids.
| 50px V3.10.10 | 50px V4.6.10 | 50px V5.6.6 | 50px V3.4.5.4 | V3.5.3.5 |
| Name | Picture | Faces | Edges | Vertices | Edges per face | Faces meeting at each vertex | |
|---|---|---|---|---|---|---|---|
| dodecahedron | (Animation) | 12 | 30 | 20 | 5 | 3 | |
| icosahedron | 50px|Icosahedron (Animation) | 20 | 30 | 12 | 3 | 5 |
| Name | picture | Faces | Edges | Vertices | Vertex configuration | ||
|---|---|---|---|---|---|---|---|
| icosidodecahedron (quasi-regular: vertex- and edge-uniform) | 50px|Icosidodecahedron (Video) | 32 | 20 triangles 12 pentagons | 60 | 30 | 3,5,3,5 | |
| truncated dodecahedron | 50px|Truncated dodecahedron (Video) | 32 | 20 triangles 12 decagons | 90 | 60 | 3,10,10 | |
| truncated icosahedron or commonly football (soccer ball) | 50px|Truncated icosahedron (Video) | 32 | 12 pentagons 20 hexagons | 90 | 60 | 5,6,6 | |
| rhombicosidodecahedron or small rhombicosidodecahedron | 50px|Rhombicosidodecahedron (Video) | 62 | 20 triangles 30 squares 12 pentagons | 120 | 60 | 3,4,5,4 | |
| truncated icosidodecahedron or great rhombicosidodecahedron | 50px|Truncated icosidodecahedron (Video) | 62 | 30 squares 20 hexagons 12 decagons | 180 | 120 | 4,6,10 | |
| Name | picture | Dual Archimedean solid | Faces | Edges | Vertices | Face Polygon |
|---|---|---|---|---|---|---|
| rhombic triacontahedron (quasi-regular dual: face- and edge-uniform) | 50px|Rhombic triacontahedron (Video) | icosidodecahedron | 30 | 60 | 32 | rhombus |
| triakis icosahedron | 50px|Triakis icosahedron (Video) | truncated dodecahedron | 60 | 90 | 32 | isosceles triangle |
| pentakis dodecahedron | 50px|Pentakis dodecahedron (Video) | truncated icosahedron | 60 | 90 | 32 | isosceles triangle |
| deltoidal hexecontahedron | 50px|Deltoidal hexecontahedron (Video) | rhombicosidodecahedron | 60 | 120 | 62 | kite |
| disdyakis triacontahedron or hexakis icosahedron | 50px|Disdyakis triacontahedron (Video) | truncated icosidodecahedron | 120 | 180 | 62 | scalene triangle |