The group 
This is the group of isometries preserving a regular Cube
Features
- Algebraic structure: semidirect product of Sym(3) and of Z2xZ2xZ2 (48 elements)
- Kind of elements
- 1 element: identity,
- 4x2 elements: rotations of order 3 around four possible axis
- 3x3 elements: rotation of order 4 around three possible axis
- 6 elements: rotation of order 2 around six possible axis
- 9 elements: plane symmetry
- 15 elements: composition of rotation and of plane symmetry
- Examples
- Cube:
- Octahedron:
