Icosahedra have twenty faces. In the image above, only twelve of those triangles are visible; the other eight have been hidden, so you can see what this solid looks like on the inside. The twelve which remain have pyritohedral symmetry — the symmetry of a volleyball.
This polyhedron has 12 faces which are regular decagons, 150 quadrilateral faces, and 80 triangular faces, 20 of which are regular. I made it using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.