In this symmetrohedron, all faces are regular, except for the green isosceles triangles. If these triangles were a little closer to being regular, this would be a near-miss to the Johnson solids, but that is not the case. I made this (starting with the last polyhedron in the post right before this one) using *Stella 4d: Polyhedron Navigator*, a program you can try for free at http://www.software3d.com/Stella.php.

# Tag Archives: symmetrohedra

# Two Symmetrohedra Featuring Decagons

Symmetrohedra are polyhedra which have some form of polyhedral symmetry, as well as having regular polygons for many (not necessarily all) of their faces. I found these two symmetrohedra while playing around with *Stella 4d: Polyhedron Navigator* — a program you can try for free at this website. Each of these symmetrohedra have 74 faces, with twelve of them being regular decagons.

# A Zonohedron Which Is Also a Symmetrohedron

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 Symmetrohedron Featuring Regular Hexagons, Squares, and Isosceles Triangles

I made this using *Stella 4d: Polyhedron Navigator*. You may try this program for yourself, for free, at http://www.software3d.com/Stella.php.

# A Symmetrohedron Featuring Regular Pentagons and Hexagons, as Well as Isosceles Trapezoids

# A 50-Faced Symmetrohedron with Cuboctahedral Symmetry

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.