The Sixth Stellation of the Triakis Octahedron Is a Three-Part Polyhedral Compound

The components of this compound are eight-faced trapezohedra. Here’s what just one of them looks like:

I made these images using Stella 4d, which you can try for free right here.

A Near-Miss to a Ring of Twelve Heptagonal Antiprisms

Twelve heptagonal antiprisms, meeting at triangular faces, can make a ring with only a small gap remaining. It’s a “near miss,” made using Stella 4d, which you can try for free right here.

A Tessellation of Regular Hexagons, Regular Heptagons, Convex Pentagons, and Large Areas of Negative Space

If you don’t want to view part of this as “negative space,” you can instead view the black regions as concave heptaicosagons (27-gons).

A Tetrahedral Symmetrohedron

This symmetrohedron has four faces which are regular hexagons, 24 which are regular pentagons, and four which are equilateral triangles. It also has twelve faces which are acute isosceles triangles, as well as twelve more which are obtuse isosceles triangles. I made it using Stella 4d, which you can try for free here.