Icosahedral Symmetry
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 × C2. The latter group is also known as the Coxeter group H3.
Read more about Icosahedral Symmetry: As Point Group, Group Structure, Fundamental Domain, Other Objects With Icosahedral Symmetry, Liquid Crystals With Icosahedral Symmetry, Related Geometries
Famous quotes containing the word symmetry:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)