This is a projection of a rotating duoprism, a four-dimensional figure, with bases which are all star pentagons. This polytope’s faces include ten of these pentagrams, and twenty-five squares. Its three-dimensional cells are ten pentagrammic prisms. I made it using Stella 4d, a program which you can try, for free, at http://www.software3d.com/Stella.php. Here is this duoprism’s three-dimensional net.
The stars on the pentagonal faces were drawn using Geometer’s Sketchpad and MS-Paint. The icosidodecahedron itself was created using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.
I ran into this on Facebook, where I posted it in 2011. That was the year before I started this blog.
The ten pentagrams meet at a common vertex in the center.
I made this by augmentation (with prisms) of the faces of a small stellated dodecahedron, using Stella 4d, which you can try for free at this website.
I made this duoprism, a four-dimensional polytope, using Stella 4d. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.
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.
RobertLovesPi.net 