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.

# Tag Archives: symmetrohedron

# 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.

# 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.

# A 122-Faced Symmetrohedron Featuring Twelve Regular Decagons and Thirty Regular Octagons

I previously blogged a different version of this symmetrohedron, one which sacrifices octagon regularity for regularity of all the other faces. Both polyhedra were created using *Stella 4d: Polyhedron Navigator,* which you can try for free right here. In this version, the twenty red hexagons are equiangular, and the sixty green faces are isosceles trapezoids.

# A Symmetrohedron with 122 Faces

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.

# 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 Symmetrohedron Featuring Regular Octagons, Pentagons, and Triangles

The only irregular faces in this polyhedron are the quadrilaterals (kites and rectangles). I made it using *Stella 4d*, which you can try for yourself — for free — at http://www.software3d.com/Stella.php.