Symmetrohedra are symmetric polyhedra with many faces regular, but not necessarily all of them. The symmetrohedron shown above is the dual of the convex hull of the compound of the great rhombicosidodecahedron and its dual, the disdyakis triacontahedron. All of its faces are regular, except for the triangles, which are scalene.
The second symmetrohedron shown here is the dual of the convex hull of the great rhombcuboctahedron and its dual, the disdyakis dodecahedron. Like its “big brother” above, all of this symmetrohedron’s faces are regular, except for the scalene triangles.
These polyhedra were made using Stella 4d, a program you can try for free at this website.
To make this, I started with the rhombic hexecontahedron (shown in this post), and then I augmented its twelve indentations with rhombic triacontahedra. I did this using Stella 4d, which you can try for free right here.
This is the rhombic hexecontahedron. Its faces are 60 rhombi with diagonals in the golden ratio. I made it by starting with a rhombic triacontahedron, then stellating it 26 times. This was done using Stella 4d, a program you can try for free at http://www.software3d.com/Stella.php.
This non-convex polyhedron can also be made using Zome, available at http://www.zometool.com, using all red struts of the same length. This was the reason I made the edges red, and the vertices white (like Zomeballs).