The group

Features

• Algebraic structure: it is the direct product of Alt(5) and of Z2, in Coxeter nomenclature it is called H3 (120 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
  • 15 elements: plane symmetry
  • 45 elements: composition of rotation and plane symmetry
• Examples
  • The Dodecahedron
    
  • The Icosahedron