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 Fifty-Faced, Zonohedrified Form of the Truncated Octahedron


A Zonohedrified Form of the Truncated Octahedron

This zonohedron has fifty faces:

  • 6 regular octagons
  • 8 regular hexagons
  • 24 squares
  • 12 equilateral octagons, the only irregular polygons needed as faces of this polyhedron

(Image created with Stella 4d — software you can try yourself at http://www.software3d.com/Stella.php.)