This is the icosahedron, one of the Platonic solids. It has twenty faces.
The polyhedron below is the rhombic enneacontahedron, a well-known zonohedron with ninety faces.
Finally, here is a polyhedron which blends these two. It has 20 + 90 = 110 faces.
I used Stella 4d: Polyhedron Navigator to make these images. You can try this program for free at http://www.software3d.com/Stella.php.