Three Symmetrohedra

Symmetrohedra are polyhedra which have many (but not all) faces regular, and have some form of polyhedral symmetry. Here’s one that has regular decagons and triangles, along with trapezoids appearing in “bowtie” pairs.

symmetroheron featuring regaular decagons.gif

The next one has regular dodecagons and decagons, along with trapezoids which closely resemble triangles, and some very thin rectangles.

122 faces 20 dodecagons 12 decagons 40 trapezoids 30 thin rectangles.gif

Finally, in the last of these three, the regular faces are dodecagons and pentagons. For the irregular faces, there are two different types of trapezoids.

152 faces 12pentqgons 20 dodecagong 60trapsand 60 difftraps.gif

All three of these were made with Stella 4d, which you can try for free right here.