There are distortions of the icosahedron that, while no longer regular, are nevertheless vertex-uniform. These are invariant under the same rotations as the tetrahedron, and are somewhat analagous to the [snub cube]? and [snub dodecahedron]?, including some forms which are chiral and some with Th-symmetry, i.e. have different planes of symmetry than the tetrahedron. The icosahedron has a large number of stellation?s, including one of the Kepler-poinsot solids and some of the regular compounds, which could be discussed here.
|