A Non-convex, Pyritohedral Dodecahedron with Non-convex Pentagonal Faces

I created this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php. Starting with the Platonic dodecahedron, I dropped the symmetry of the model down from icosahedral to tetrahedral, then stellated it six times. I also put the resulting polyhedron into “rainbow color mode” before making this .gif image.

My 2019 Birthday Star

I was born 51 years ago today. To mark the occasion, here’s a 51-pointed star. It’s made of {17/7} heptadecagrams repeated 3 times, and with their edges extended as lines, in three different colors. This works because 51 = (17)(3).

A 50-Faced Symmetrohedron with Cuboctahedral Symmetry

This image was created using Stella 4d, software you may try for yourself (for free) at http://www.software3d.com/Stella.php.

In this symmetrohedron, the red, blue, and green faces are regular polygons. Only the yellow isosceles trapezoids are irregular.

Zonohedra Based on the Pentagonal Dipyramid

Here’s a pentagonal dipyramid. It’s one of the Johnson solids.

j13

The polyhedra-manipulation software I use, Stella 4d (available as a free trial download right here), lets the user make zonohedra from various “seed” polyhedra. When I made one with zones based on the vertices of the pentagonal dipyramid, a decagonal prism was the result. This surprised me; I wasn’t expecting to see a familiar polyhedron.

zonohedrified penta dipyramid v

Other selections gave me the results I expected: polar zonohedra I had never seen before. Here’s the one based on the edges of the pentagonal dipyramid.

zonohedrified penta dipyramid e

The next one is based on the pentagonal dipyramid’s faces.

zonohedrified penta dipyramid f

Here’s one based on vertices and edges:

zonohedrified penta dipyramid v e

This next one is based on vertices and faces.

The next one is based on edges and faces.

Finally, here’s the last one, with zones based on the faces, edges, and vertices of a pentagonal dipyramid.

A Symmetrohedron with Tetrahedral Symmetry

Symmetrohedra are symmetrical, convex polyhedra which contain many faces (not necessarily all) which are regular polygons. In this symmetrohedron, the hexagons and triangles are regular, while the quadrilaterals are isosceles trapezoids. I made this symmetrohedron using Stella 4d, a program you can try for free at this website.

symmetrohedron featuring 10 reg hexagons and 4 eqtriangles and 12 isos traps

A Compound of a Slightly-Truncated Icosahedron and the Rhombic Triacontahedron

This image was created using Stella 4d: Polyhedron Navigator, which you can try out for free at http://www.software3d.com/Stella.php.