The Rhombic Octagonoid, a Zonohedron With Ninety Faces

To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to the rhombic enneacontahedron, with thirty equilateral octagons replacing the thirty narrow rhombic faces of that polyhedron.

I’ve run into this polyhedron from time to time, and have also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here) of a single strut-length (short, medium, or long). I thought it needed a name, so I made one up.

9 thoughts on “The Rhombic Octagonoid, a Zonohedron With Ninety Faces

  1. Pingback: A Partial Faceting of the Rhombic Octagonoid |

  2. It is truly a zonohedron of 240 rhombic faces. The octagons have 6 rhombi co-planar in each.
    (5*12)+(6*30) = 240
    See the 16th row of Pascal’s triangle: 1,16,120,560, . . .
    16 unique directions, 120 parallel faces, for a total of 240
    560 rhombic hexahedron define the interior


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