The 122 faces are twenty blue, irregular hexagons; thirty red, irregular hexagons; 60 rectangles, and twelve regular pentagons.
Software credit: just visit http://www.software3d.com.stella.php and look for the free trial download of Stella 4d, the program I used to make this rotating image.
The dodecagons are in the same planes as a cube’s faces, so there are six of them. Also, this could be constructed via an unusual truncation of the cube, using three different truncation-planes at each vertex. This polyhedron has thirty faces: the six dodecagons, and twenty-four kites (in eight sets of three).
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this polyhedron.
Software credit: see http://www.software3d.com/stella.php for a free trial download of Stella 4d, the software I used to construct this cluster, three deep, of octahedra.
Software credit: you can try the software I used to make this at http://www.software3d.com/stella.php.
To create this, a central rhombicosidodecahedron had each of its faces augmented by pyramids, each of which uses only equilateral triangles for lateral faces.
Software credit: The program used to make this image, Stella 4d, may be tried for free at http://www.software3d.com/stella.php.