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.

Four Symmetrohedra with Tetrahedral Symmetry

Symmetrohedra are polyhedra with some form of polyhedral symmetry, and many (not necessarily all) regular faces. The first two symmetrohedra here each include four regular enneagons as faces.

The next two symmetrohedra each include four regular dodecagons as faces.

All four of these were made using Stella 4d, which you can try out for free at http://www.software3d.com/Stella.php.

Four Symmetrohedra

Symmetrohedra are polyhedra with some form of polyhedral symmetry, all faces convex, and many (but not all) faces regular. Here are four I have found using Stella 4d, a polyhedron-manipulation program you can try for yourself at http://www.software3d.com/Stella.php.

octagons and elongates dodecagons.gif

Octagon-dominated zonohedron

regular decagons and triangles, plus elongated octagons.gif
dual of GRID and dual's compound's convex hull 182 faces incl 12 deca 20 hexa 30 squares and 120 triangles

The second of these symmetrohedra is also a zonohedron, and is colored the way I usually color zonohedra, coloring faces simply by number of sides per face. That is why some of the red octagons in that solid are regular, while others are elongated. The other three symmetrohedra are colored by face type, with the modification that the fourth one’s scalene triangles are all given the same color.

These symmetrohedra were all generated using Stella 4d, a program you may try for yourself at http://www.software3d.com/Stella.php.