12 
12 
12 
12 30 
12 30
| F = # of faces E = # of edges V = # of vertices |
| Model | F | E | V | Shapes |
| Icosahedron | ||||
|
| 20 | 30 | 12 | 20 |
| Truncated Icosahedron | ||||
|
| 32 | 90 | 60 | 20 12 |
| Icosadodecahedron | ||||
|
| 32 | 60 | 30 | 20 12 |
| Truncated Dodecahedron | ||||
|
| 32 | 90 | 60 | 20 12 |
| Dodecahedron | ||||
|
| 12 | 30 | 20 | 12 |
| Rhombicosadodecahedron | ||||
|
| 62 | 120 | 60 | 20 12 30 |
| Rhombitruncated Icosadodechedron | ||||
|
| 62 | 180 | 120 | 20 12 30 |
= blue regular decagon (10-sides)
We have picked icosahedron and rhombicosadodecahedron to show the 2-, 3-, and 5- fold symmetries in this group. In each of the polyhedra below, we have highlighted some planes of reflection symmetry to show the folds of symmet$
| 2-fold | 3-fold | 5-fold |
| 
|  |
| 
|  |