A Polyhedron Featuring Sixty Regular Heptagons

In addition to the sixty heptagons, there are twelve regular pentagons and sixty quadrilaterals in this polyhedron, along with 380 triangles of various shapes and sizes. That’s 512 faces in all.

I used Stella 4d: Polyhedron Navigator to make this. You may try this program, for free, at http://www.software3d.com/Stella.php.

A Fifty-Faced Polyhedron Featuring Eighteen Regular Octagons

In addition to the eighteen regular octagons, this polyhedron also has eight equiangular hexagons and twenty-four isosceles trapezoids among its fifty faces. I made it using Stella 4d, which you can try, for free, right here.

Repeated Augmentations of a Dodecahedron With More and More Dodecahedra

Here’s a single dodecahedron.

A new “cluster polyhedron” can be made by augmenting each pentagonal face with another dodecahedron.

If you can do it once, you can do it again, augmenting each pentagon with a new dodecahedron.

Once more.

I made these polyhedral clusters using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

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.