A Symmetrohedron Featuring Twenty Equilateral Triangles, Twelve Regular Decagons, and Sixty Isosceles Triangles

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

Two Chiral Symmetrohedra Derived From the Snub Dodecahedron

Each of these symmetrohedra has 302 faces. The one above was created by using the “morph duals by expansion” function, on the snub dodecahedron, in Stella 4d, the program I use to manipulate polyhedra (go here if you want to download a free trial of this software). It has twelve regular pentagons, sixty almost-square rectangles, and eighty equilateral triangles, along with ninety more obviously non-square rectangles, and sixty irregular pentagons.

I next used Stella’s “try to make faces regular” function, which produced this result:

This second polyhedron has 72 regular pentagons as faces, along with 20 equilateral triangles, 60 narrow isosceles triangles, and 150 irregular quadrilaterals. That’s 92 regular faces, in each of these two polyhedra.

A Chiral Symmetrohedron Featuring Two Dozen Regular Pentagons, Eight Equilateral Triangles, and Six Squares

This symmetrohedron has 122 faces. They are: (1) twenty-four blue, regular pentagons; (2) six green squares, (3) eight pink, equilateral triangles, (4) sixty red, irregular quadrilaterals, and (5) twenty-four yellow, scalene triangles. I made it, starting with the snub cube, using Stella 4d, a program you may try for free at this website: http://www.software3d.com/Stella.php.

A Symmetrohedron With 152 Faces

The 152 faces of this symmetrohedron include twelve regular decagons, twenty regular hexagons, and 120 irregular quadrilaterals arranged in thirty groups of four quads each. I made it using Stella 4d, which you can download here as a free trial version.

Chiral Symmetrohedron #2

In the last post here, I displayed a chiral symmetrohedron derived from the snub dodecahedron, and today I am presenting its “little brother,” which is derived from the snub cube. Both models were created using the “morph duals by truncation” function of Stella 4d: Polyhedron Navigator, a program you can download and try, for free, at this website. This newer solid contains six squares, 32 equilateral triangles, and 24 irregular pentagons, for a total of 62 faces.

A Chiral Symmetrohedron

This symmetrohedron was derived from the snub dodecahedron. It contains twelve regular pentagons and sixty irregular pentagons, as well as eighty equilateral triangles, for a total of 152 faces. I made it using Stella 4d (with the “morph duals by truncation” function), a program you can download and try, for free, at this website.

A Symmetrohedron Derived From the Great Rhombicosidodecahedron

This solid has all the faces of the great rhombicosidodecahedron, plus 120 scalene triangles. I made it using Stella 4d, which you can try for free right here.

Regular Octadecagons As Faces of Symmetrohedra

I tried to make a symmetrohedron using regular octadecagons and regular decagons, but that combination forces the octadecagons to overlap, and that causes the would-be symmetrohedron to be non-convex.

I tried to augment these octadecagons with antiprisms, and then form the convex hull of the result. Here’s what I found:

I made these using Stella 4d, which you can try for free right here.