Each of these symmetrohedra has 302 faces. The one above was created by using the “morph duals by expansion” function, on the snub dodecahedron, in* Stella 4d*, the program I use to manipulate polyhedra (go here if you want to download a free trial of this software). It has twelve regular pentagons, sixty almost-square rectangles, and eighty equilateral triangles, along with ninety more obviously non-square rectangles, and sixty irregular pentagons.

I next used Stella’s “try to make faces regular” function, which produced this result:

This second polyhedron has 72 regular pentagons as faces, along with 20 equilateral triangles, 60 narrow isosceles triangles, and 150 irregular quadrilaterals. That’s 92 regular faces, in each of these two polyhedra.

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I have enjoyed your work for many years.

Thank you for posting them

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You’re welcome!

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These are so interesting!

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