Rhombicosidodecahedron

This is a combination of a dodecahedron and an icosahedron (a Minkowski join in fact).

It seems to be called a Rhombicosidodecahedron according to wikipedia.
https://en.wikipedia.org/wiki/Rhombicosidodecahedron

I.e. it has all 12 pentagons of a dodecahedron, in the right places, and all 20 triangles of an icosahedron in the right places, and squares in between.

62 sides altogether.

Quite fun.