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.

Two Versions of a Fifty-Faced Symmetrohedron

The first version of this polyhedron was created by zonohedrification of a tetrahedron, based on that solid’s faces, edges, and vertices. All of its faces are regular polygons, except for the red hexagons.

I used Stella 4d: Polyhedron Navigator to make these (and you can try that program for free at this website). The next thing I did was to apply Stella‘s “try to make faces regular” function to the solid above, producing the one shown below. In this second version, the only irregular faces are the yellow isosceles trapezoids.

A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs

symmetrohedron featuring heptagons hexagons and pentagons

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

symmetrohedron featuring heptagons hexagons and pentagons net

This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

A Symmetrohedron Featuring Regular Heptagons and Hexagons, Along with Irregular Quadrilaterals and Triangles

symmetrohedron

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

symmetrohedron net

This particular symmetrohedron features 12 faces which are regular heptagons, and 8 faces which are regular hexagons. The irregular faces are 12 isosceles triangles, 24 isosceles trapezoids, and 6 rectangles, for a total of 62 faces. It has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.

A Fifty-Faced Symmetrohedron Featuring Twenty Regular Hexagons and Six Squares, Along with 24 Isosceles Trapezoids

Symmetrohedra are symmetrical polyhedra which have many (but not necessarily all) faces regular. The only irregular faces in this polyhedron are the blue isosceles trapezoids.

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

A Symmetrohedron Featuring Twelve Regular Pentagons, Thirty Regular Octagons, and Twenty Equilateral Triangles

In addition to the sixty-two regular faces, this polyhedron also has two sets of sixty isosceles trapezoids each, shown in different shades of blue. That’s 182 faces in all. I made it using Stella 4d, which you can try for free at www.software3d.com/Stella.php.