A Tetrahedral Symmetrohedron

This symmetrohedron has four faces which are regular hexagons, 24 which are regular pentagons, and four which are equilateral triangles. It also has twelve faces which are acute isosceles triangles, as well as twelve more which are obtuse isosceles triangles. I made it using Stella 4d, which you can try for free here.

A Symmetrohedron Derived from the Rhombic Dodecahedron

To make this symmetrohedron, I augmented the faces of a rhombic dodecahedron with prisms, then formed the convex hull of the result. All faces except for the red rhombi are regular. This was made using Stella 4d, which you can try for free here.

A 50-Faced Symmetrohedron Which Is Also a Zonohedron

I made this polyhedron by creating a zonohedron based on the edges and faces of the truncated tetrahedron. Only the blue hexagons are irregular. Stella 4d was used in its creation, and you may try this program for free at http://www.software3d.com/Stella.php.

A Symmetrohedron Which Is Also a Zonohedron

I made this by zonohedrificaton of an octahedron, using its faces, edges, and vertices, and software called Stella 4d, which you can try for free right here.

This polyhedron has six regular octagons (red), a dozen octagons which are merely equilateral (yellow), eight regular hexagons, and 24 squares.

A Symmetrohedron With 182 Faces

This symmetrohedron’s regular faces are twelve pentagons, thirty octagons, and twenty triangles. Its irregular faces include sixty yellow isosceles trapezoids, as well as sixty blue isosceles trapezoids. That makes 182 faces in all.

I used Stella 4d: Polyhedron Navigator to make this, and you can try this program yourself, as a free trial download, at http://www.software3d.com/Stella.php.

A Twenty-Faced Symmetrohedron With Four Equilateral Triangles, Four Regular Hexagons, and Six “Bowtie” Pairs of Isosceles Trapezoids as Faces

I made this using Stella 4d, which you can try for yourself at this website.

Two Symmetrohedra

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.

A Symmetrohedron Featuring Eight Regular Hexagons, Six Squares, and 24 Isosceles Triangles

The isosceles triangles in this polyhedron have legs which are each 22.475% longer than their bases. I made this by creating the dual of the convex hull of the base/dual compound of the truncated octahedron, using a program called Stella 4d, which you can try for free right here.

A Symmetrohedron Featuring Squares, Regular Hexagons, and “Bowtie” Pairs of Trapezoids

This symmetrohedron has eight hexagonal faces, six square faces, and twelve pairs of trapezoids, for a total of 38 faces. I made it by using Stella 4d to modify a truncated octahedron. You may try this program for free at www.software3d.com/Stella.php.