# 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 I’ve also had students make it. It is the largest zonohedron which can be built using only red and yellow Zome (available here). I thought it needed a name, so I made one up.

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

1. Are those octagons irregular?

Like

• Yes, they are. They are also zonogons.

Like

• What’re zonogons to be exact? The Wiki page is quite short and not very detailed (in my opinion).

Like

• Zonogons are polygons, with even numbers of sides, in which opposite sides are both parallel and congruent.

Like

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

Like

• Interesting!

Like

• I started with an dodecahedron, then made a zonohedron based on that solid’s faces and vertices.

Like