This polyhedron contains 72 regular polygons, 20 equilateral triangles, and 302 faces in all. But where did it come from?

I made it, starting with the snub dodecahedron, using *Stella 4d* (available here).

This is the dual of the snub dodecahedron. It is called the pentagonal hexecontahedron.

There are various ways of combining polyhedra with their duals, and the one I used here is called morphing duals by expansion. Here’s the 50%-morphed version.

The next step was to use Stella’s “try to make faces regular” function, which worked best for the 72 pentagonal faces, as well as the twenty of the equilateral triangles.

From there, simple changes of face-color produced the polyhedron shown at the top of this post.

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Are all the rhombi the same? Are the trapezoids isosceles?

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I don’t think there are any rhombi or trapezoids.

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