A regular icosahedron has 60 rotational
(or orientation-preserving) symmetries,
and a symmetry order of 120 including
transformations that combine a reflection
and a rotation. A regular dodecahedron
has the same set of symmetries, since it is
the dual of the icosahedron.

The set of orientation-preserving symmetries
forms a group referred to as A5 (the alternating
group on 5 letters), and the full symmetry
group (including reflections) is the product
A5 × Z2. The latter group is also known
as the Coxeter group H3, and is also represented
by Coxeter notation and a Coxeter diagram.