A Dodecahedron with Four Symetrically-Truncated Vertices

dodeca with 4 verts truncated tet symm

Dodecahedra have icosahedral (also called icosidodecahedral) symmetry. In the figure above, this symmetry is changed to tetrahedral, by truncation of four vertices with positions corresponding to the vertices (or, instead, faces) of a tetrahedron. The interchangeability of vertices and faces for the tetrahedron is related to the fact that the tetrahedron is self-dual.

[Image created using Stella 4d, available here.]

Multiple Octahedra, in a Rotating Cluster with Tetrahedral Symmetry


Multiple Octahedra, in a Rotating Cluster with Tetrahedral Symmetry

I created this cluster using Stella 4d: Polyhedron Navigator. This program is available at http://www.software3d.com/Stella.php.