The group 
This is the group of rotation preserving a regular Dodecahedron
Features
- Algebraic structure: it is the alternating group on 5 elements (60 elements)
- Kind of elements
- 1 element: identity,
- 6x4 elements: rotation of order 5 on six possible axis
- 10x2 elements: rotation of order 3 on ten possible axis
- 15 elements: rotation of order 2 on 15 possible axis
- Examples
- First Fullerene of symmetry I:
