To make the first of these variations, above, I augmented each triangular face of a snub dodecahedron with an antiprism 2.618 times as tall as the triangles’ edge length, and then took the convex hull of the result. The other polyhedra shown, below, were obtained by various other manipulations of the snub dodecahedron, all performed using a program called *Stella 4d: Polyhedron Navigator*, which you can try right here.

The variant above looked like it needed a name, so I called it an expanded snub truncated dodecahedron. As for the one below, it is one of many facetings of the snub dodecahedron.

Finally, the last figure shown (stumbled upon during a “random walk” with *Stella*) is one of many possible figures which are non-convex relatives of the snub dodecahedron.

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