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.

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