# A Concave Polyhedron Featuring Eight Regular Dodecagons

This 110-faced polyhedron has, in addition to the eight regular dodecagons, six rectangles, and 96 triangles. I made it using Stella 4d, a program you can try for free, as a demo version, at http://www.software3d.com/Stella.php. I wish I could remember how I made it!

Fortunately, I have many friends who are more knowledgeable than I, when it comes to mathematics. Perhaps one of them will be able to solve this mystery.

# 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.

# Six Non-Convex Polyhedra with Cuboctahedral Symmetry

Each of these polyhedral images (any of which may be enlarged with a click) was created using Stella 4d: Polyhedron Navigator, and this program may be tried for free at http://www.software3d.com/Stella.php.

Also, a question, for regular readers of my blog — you have probably noticed that this post has a different format, but it’s just an experimental thing I’m trying out.

Do you prefer this style of polyhedra-post, or the format I usually use?

# Six Random Starsplosions of Non-Convex Polyhedra with Cuboctahedral Symmetry

All of these were made using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.

# Non-Convex and Cuboctahedral

Created with Stella 4d, available here.

# A Non-Convex Polyhedron with Cuboctahedral Symmetry

I used Stella 4d to make the polyhedron above, and you can try this software for yourself here.

# A Non-Convex “Cousin” of the Cuboctahedron

My guess is that this is a faceting of the cuboctahedron, but I didn’t use faceting when I made it with Stella 4d (a program you can try here), so I am not sure about this. Based on its appearance, however, it is clearly related, in some manner, to the cuboctahedron, for the cuboctahedron is its convex hull.

# A Non-Convex Polyhedron with Sixty Non-Convex Pentagonal Faces

Created using Stella 4d:  Polyhedron Navigator, available for purchase (with a free trial download available, first) at www.software3d.com/Stella.php.