Four Symmetrohedra

Symmetrohedra are polyhedra with some form of polyhedral symmetry, all faces convex, and many (but not all) faces regular. Here are four I have found using Stella 4d, a polyhedron-manipulation program you can try for yourself at

octagons and elongates dodecagons.gif

Octagon-dominated zonohedron

regular decagons and triangles, plus elongated octagons.gif
dual of GRID and dual's compound's convex hull 182 faces incl 12 deca 20 hexa 30 squares and 120 triangles

The second of these symmetrohedra is also a zonohedron, and is colored the way I usually color zonohedra, coloring faces simply by number of sides per face. That is why some of the red octagons in that solid are regular, while others are elongated. The other three symmetrohedra are colored by face type, with the modification that the fourth one’s scalene triangles are all given the same color.

These symmetrohedra were all generated using Stella 4d, a program you may try for yourself at

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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