The faces of this polyhedron include twelve regular decagons, as well as sixty convex pentagons. I made it using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.

To make this polyhedron using Stella 4d (available here), I started with the dodecahedron, dropped the symmetry of the model down to tetrahedral, and then stellated it twice.

This polyhedron has tetrahedral symmetry, and eight faces. Four of them are equilateral triangles, while the other four are 6/2-gons. I made it by modification of the truncated tetrahedron, using Stella 4d, which you can try for yourself, for free, at http://www.software3d.com/Stella.php.