# The {5/2}, {5,2} Duoprism

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.

# A Starry Icosidodecahedron

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.

# Three Pentagrams (from 2011)

I ran into this on Facebook, where I posted it in 2011. That was the year before I started this blog.

# Ten Pentagrams

The ten pentagrams meet at a common vertex in the center.

# Twelve Pentagrammic Prisms

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.

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

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.