There Are Many Faceted Versions of the Dodecahedron. This One Is the Dual of the Third Stellation of the Icosahedron.

Faceted Dodeca

The twelve purple faces of this faceted dodecahedron show up on Stella 4d‘s control interface as {10/4} star decagons, which would make them each have five pairs of two coincident vertices. I’m informally naming this special decagon-that-looks-like-a-pentagram (or “star pentagon,” if you prefer) the “antipentagram,” for reasons which I hope are clear.

Stella 4d, the program I use to make most of my polyhedral images, may be tried for free at http://www.software3d.com/Stella.php.

The Rhombic Dodecahedron’s Third Stellation

Image

The Rhombic Dodecahedron's Third Stellation

Above is this polyhedral stellation in three colors. If every face is given its own color, though, except for parallel faces, it looks like this (click to enlarge):

RD stellation 3rd colors b

I made both images using Stella 4d, a program you can find at http://www.software3d.com/Stella.php.