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.