This symmetrohedron includes, as faces, eight regular hexagons, six squares, and 24 isosceles triangles. I made it using *Stella 4d*, which you can try for free at this website.

# Tag Archives: symmetrohedra

# A Symmetrohedron Which Is Also a Zonohedron

I made this by zonohedrificaton of an octahedron, using its faces, edges, and vertices, and software called *Stella 4d,* which you can try for free right here.

This polyhedron has six regular octagons (red), a dozen octagons which are merely equilateral (yellow), eight regular hexagons, and 24 squares.

# 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

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.

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

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.

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.