I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

I made this using Stella 4d, which you can try for free at this website.

The model above shows the rhombic dodecahedron colored with one color per face, unless those faces are parallel. The one below shows this solid in “rainbow color mode.”

I made both of these using Stella 4d: Polyhedron Navigator. You can try this program for free at http://www.software3d.com/Stella.php.

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

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

This, above, is the pentagonal icositetrahedron — one of the Catalan solids, and the dual of the snub cube. If faceting is used to remove square-based pyramids, the result is the solid shown below — a chiral polyhedron with six square faces, and 24 faces which are isosceles trapezoids.

I use a program called Stella 4d: Polyhedron Navigator (available here) to perform these polyhedral manipulations. This program has a “try to make faces regular” function, and the solid shown below is the result of using that function on the polyhedron shown above.

The “try to make faces regular” function appeared at first to leave the squares as squares (which it did), but turn the trapezoids into kites (which it did not; the yellow quadrilaterals’ longer sides are actually of two slightly different lengths). Lastly, I used Stella to create the compound of the polyhedron above and its dual. The result is shown below.

I made this chiral polyhedron using Stella 4d, which you can try for yourself — free — at this website. It is a faceted form of the pentagonal hexecontahedron, which is the dual of the snub dodecahedron.