Four Symmetrohedra with Tetrahedral Symmetry

Symmetrohedra are polyhedra with some form of polyhedral symmetry, and many (not necessarily all) regular faces. The first two symmetrohedra here each include four regular enneagons as faces.

The next two symmetrohedra each include four regular dodecagons as faces.

All four of these were made using Stella 4d, which you can try out for free 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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2 Responses to Four Symmetrohedra with Tetrahedral Symmetry

  1. ben3nett says:

    Hi, RLPi, I am curious about the color-element assignments you use in your modeling. Vertices are blue and the edges are yellow. FACES that are squares, octagons, and cubes are red. Edges are yellow, Triangles are hexagons, and dodecagons are Blue, Faces; pentagons and decagons are magenta or violet. The color systems of light and the ‘kundalini’s’ colors and forms of its seven chakras apply to the polyhedra language. They also reflect the qualities of the five elements of matter as well. Green being the blend of blue and yellow would be the product of symmetry operations involving the transformations revealed with vertices, faces, and edges. Vertices on their own are blue. When they are truncated adjacent ‘colors’ could also be blended as well.


    • The software I use is extremely flexible with regard to color. Lately, I’ve been using metallic colors for edges and vertices, and primary colors for faces, but I can change that any time I wish to.


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