This symmetrohedron has 122 faces. They are: (1) twenty-four blue, regular pentagons; (2) six green squares, (3) eight pink, equilateral triangles, (4) sixty red, irregular quadrilaterals, and (5) twenty-four yellow, scalene triangles. I made it, starting with the snub cube, using Stella 4d, a program you may try for free at this website: http://www.software3d.com/Stella.php.