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.