Each of these symmetrohedra has 302 faces. The one above was created by using the “morph duals by expansion” function, on the snub dodecahedron, in Stella 4d, the program I use to manipulate polyhedra (go here if you want to download a free trial of this software). It has twelve regular pentagons, sixty almost-square rectangles, and eighty equilateral triangles, along with ninety more obviously non-square rectangles, and sixty irregular pentagons.

I next used Stella’s “try to make faces regular” function, which produced this result:

This second polyhedron has 72 regular pentagons as faces, along with 20 equilateral triangles, 60 narrow isosceles triangles, and 150 irregular quadrilaterals. That’s 92 regular faces, in each of these two polyhedra.

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.