This is the rhombic triacontahedron, one of the Catalan solids.

Now here’s the same polyhedron, but with the three-valent vertices truncated, exposing twenty triangular faces.

Here’s what it looks like with only the twelve five-valent vertices truncated.

Finally, here’s the fully truncated rhombic triacontahedron.

I created these polyhedra using *Stella 4d*, a program you can try for free right here.

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