| Symmetry | Asymmetry | ||
Twofold | Threefold | Fivefold | ||
Icosahedron | Unequilateral hexagon | Regular hexagon | Regular decagon | -- |
Dodecahedron | Unequilateral hexagon | Hexagon-like dodecagon | Regular decagon | (two forms) |
Pentakis dodecahedron | regular decagon | Regular decagon | Regular decagon | -- |