A Twice-Zonohedrified Dodecahedron

If one starts with a dodecahedron, and then creates a zonohedron based on that solid’s vertices, the result is a rhombic enneacontahedron.

If, in turn, one then creates a new zonohedron based on the vertices of this rhombic enneacontahedron, the result is this 1230-faced polyhedron — a twice-zonohedrified dodecahedron. Included in its faces are thirty dodecagons, sixty hexagons, and sixty octagons, all of them equilateral.

Stella 4d: Polyhedron Navigator was used to perform these transformations, and to create the rotating images above. You can try this program for yourself, free, at http://www.software3d.com/Stella.php.

A Twice-Truncated Cube

twice-truncated cube

Truncating a cube once yields an Archimedean solid with six octagonal faces, and eight triangular faces, all regular. A second truncation can be made to produce the solid shown above. It also has, as faces, six regular octagons and eight equilateral triangles — and, in addition, twenty-four isosceles triangles.

I made this using Stella 4d, software you can try for yourself at www.software3d.com/Stella.php.