This symmetrohedron has the six regular octagons, eight regular hexagons, and twelve squares of its “parent,” the great rhombicuboctahedron. It was modified by using the “morph duals at 50% by tilting to rectify” function, twice. This left the resulting polyhedron with additional faces: 72 trapezoids (24 each, of three types), and 48 scalene triangles. That’s 146 faces in all. I made it using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php.

This symmetrohedron has the twelve regular decagons, twenty regular hexagons, and thirty squares of its “parent,” the great rhombicosidodecahedron. It was modified by using the “morph duals at 50% by tilting to rectify” function, twice. This left the resulting polyhedron with additional faces: 180 trapezoids (60 each, of three types), and 120 scalene triangles. That’s 362 faces in all. I made it using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php.

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

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.

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.

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.

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.

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.

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.