Six Convex Polyhedra Featuring Convex Dodecagons, Some of Which Are Regular

Individual images may be enlarged with a click. They were created using Stella 4d: Polyhedron Navigator, which may be tried for free at


The Pentagonal Hexacontahedron, and Related Polyhedra


The Pentagonal Hexacontahedron

As the dual of the snub dodecahedron, which is chiral, this member of the Catalan Solids is also chiral — in other words, it exists in left- and right-handed versions, known an entantiomers. They are mirror-images of each other, like left and right gloves or shoes. Here’s the other one, by comparison:

Penta Hexeconta enantiomer

It is always possible to make a compound, for a chiral polyhedron, from its two enantiomers. Here’s the one made from the two mirror-image pentagonal hexacontahedra shown above:

Compound of enantiomorphic pair

Stellating this enantiomorphic-pair-compound twenty-one times produces this interesting result:


And, returning to the unstellated enantiamorphic-pair-compound, here is its convex hull:

Convex hull

This convex hull strikes me as an interesting polyhedron in its own right, so I tried stellating it several times, just to see what would happen. Here’s one result, after seventeen stellations:


Software credit:  I made these rotating images using Stella 4d:  Polyhedron Navigator. That program may be bought at, and has a free “try it before you buy it” trial download available at that site, as well. I also used Geometer’s Sketchpad and MS-Paint to produce the flat purple-and-black image found on faces near the top of this post (and, by itself, in the previous post on this blog), but I know of nowhere to get free trial downloads of these latter two programs.