In this symmetrohedron, the red, blue, and green faces are regular polygons. Only the yellow isosceles trapezoids are irregular.

# Tag Archives: symmetrohedron

# A Symmetrohedron with Tetrahedral Symmetry

Symmetrohedra are symmetrical, convex polyhedra which contain many faces (not necessarily all) which are regular polygons. In this symmetrohedron, the hexagons and triangles are regular, while the quadrilaterals are isosceles trapezoids. I made this symmetrohedron using *Stella 4d*, a program you can try for free at this website.

# A Symmetrohedron

Symmetrohedra are symmetrical polyhedra which have many, but not all, faces regular. I just found one which has square faces, regular hexagons, regular octagons, and a bunch of scalene triangles as the irregular faces.

To form this polyhedron, I started with the great rhombcuboctahedron, then formed its base/dual compound. I then took the convex hull of this compound, and then formed the dual of that convex hull, producing the polyhedron you see above. All of this was done using *Stella 4d: Polyhedron Navigator*, which you can try for free at http://www.software3d.com/Stella.php.

# Four Symmetrohedra with Tetrahedral Symmetry

Symmetrohedra are polyhedra with some form of polyhedral symmetry, and many (not necessarily all) regular faces. The first two symmetrohedra here each include four regular enneagons as faces.

The next two symmetrohedra each include four regular dodecagons as faces.

All four of these were made using *Stella 4d*, which you can try out for free at http://www.software3d.com/Stella.php.

# Two Symmetrohedra Which Feature Enneagons

These two symmetrohedra were created using *Stella 4d*, software you can try for free right here.

# Three Symmetrohedra

Symmetrohedra are polyhedra which have many (but not all) faces regular, and have some form of polyhedral symmetry. Here’s one that has regular decagons and triangles, along with trapezoids appearing in “bowtie” pairs.

The next one has regular dodecagons and decagons, along with trapezoids which closely resemble triangles, and some very thin rectangles.

Finally, in the last of these three, the regular faces are dodecagons and pentagons. For the irregular faces, there are two different types of trapezoids.

All three of these were made with *Stella 4d*, which you can try for free right here.

## A Symmetrohedron Featuring Regular Hexadecagons and Regular Hexagons

### Image

I made this using *Stella4d*, which you can try for free right here.