A Symmetrohedron Featuring Regular Octagons, Pentagons, and Triangles

The only irregular faces in this polyhedron are the quadrilaterals (kites and rectangles). I made it using Stella 4d, which you can try for yourself — for free — at http://www.software3d.com/Stella.php.

A Zonohedron Which Is Also a Symmetrohedron

I made this using Stella 4d, which you can try for free at http://www.software3d.com/Stella.php.

This zonohedron is based on the icosidodecahedron / rhombic triacontahedron compound — more specifically, on its edges. Twelve faces are regular decagons, twenty are regular hexagons, sixty are squares, and the only irregular faces are the thirty equilateral octagons. That’s 122 faces in all.

A 50-Faced Symmetrohedron with Cuboctahedral Symmetry

This image was created using Stella 4d, software you may try for yourself (for free) at http://www.software3d.com/Stella.php.

In this symmetrohedron, the red, blue, and green faces are regular polygons. Only the yellow isosceles trapezoids are irregular.

A Symmetrohedron with Tetrahedral Symmetry

Symmetrohedra are symmetrical, convex polyhedra which contain many faces (not necessarily all) which are regular polygons. In this symmetrohedron, the hexagons and triangles are regular, while the quadrilaterals are isosceles trapezoids. I made this symmetrohedron using Stella 4d, a program you can try for free at this website.

symmetrohedron featuring 10 reg hexagons and 4 eqtriangles and 12 isos traps

A Symmetrohedron

Symmetrohedra are symmetrical polyhedra which have many, but not all, faces regular. I just found one which has square faces, regular hexagons, regular octagons, and a bunch of scalene triangles as the irregular faces.

To form this polyhedron, I started with the great rhombcuboctahedron, then formed its base/dual compound. I then took the convex hull of this compound, and then formed the dual of that convex hull, producing the polyhedron you see above. All of this was done using Stella 4d: Polyhedron Navigator, which you can try for free at http://www.software3d.com/Stella.php.