A Concave Polyhedron Featuring Eight Regular Dodecagons

110 faces 8 dodec 6 rectangles 96 triangles

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.

Three Non-convex Polyhedra with Cuboctahedral Symmetry

These were all created using Stella 4d, a program you can try — for free — at http://www.software3d.com/Stella.php.

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.

Here’s a net for this solid. To build it, you’ll need six copies of this net.

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

Compound of enantiomorphic pair

Faceted Trunc Octa dual of the compound

Small Cubicubocta dual the small hexacronic icositetrahedronUnnamed Dual

stellated disdyakis dodecahedronStellated Penta Icositetra

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

nc and coCreated with Stella 4d, available here.

A Non-Convex Polyhedron with Cuboctahedral Symmetry

co symm and nc

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

appears to be a facted 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.

Four Non-Convex Polyhedra with Icosidodecahedral Symmetry

Unnamed Dhgual

pretty

Dual of Augmented Convex hull

unholy messl

All of these were made with Stella 4d, a program you can find at http://www.software3d.com/Stella.php.

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

Sixty nonconvex pentagons as faces of a nonconvex polyhedron

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