The hexagons and squares in this polyhedron are regular; only the isosceles trapezoids are not. I made it using *Stella 4d*, which you can try for free right here.

# Tag Archives: symmetrohedron

# A Spiky Symmetrohedron

This was a normal symmetrohedron, until I augmented its trapezoidal faces with pyramids. I did this using *Stella 4d: Polyhedron Navigator*, which you can try out for free at http://www.software3d.com/Stella.php.

# A Fifty-faced Zonohedron Which Is Also a Symmetrohedron

I created this symmetrohedron as the zonohedron based on the faces, edges, and vertices of the tetrahedron. It has fifty faces: thirty squares, plus eight regular hexagons, and twelve merely-equilateral hexagons. I made it using *Stella 4d*, which you can try for free at this website.

# A Symmetrohedron Which Is Also a “Near Near Miss”

I’ve spent a lot of time over the years looking for “near misses” to the Johnson Solids, and I’ve found two of them in all that time, starting in 2003. This isn’t one, for it has an edge length deviation of about 11%, which is too much to get overly excited about. It is, however, a symmetrohedron. The hexagons, pentagons, and yellow triangles are all regular; it’s only the blue triangles which are irregular (and isosceles). It has 122 faces in all. I think I can also say, with confidence, that it is a “near near miss.” In other words, it’s nearly a near-miss to the Johnson Solids. Confused yet? I know I am.

I made this using *Stella 4d*, software you can try for free at http://www.software3d.com/Stella.php.

# A Symmetrohedron Featuring Four Regular Enneagons, Four Regular Hexagons, and Six Pairs of “Bowtie” Isosceles Trapezoids

I made this twenty-faced polyhedron using *Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php.

# A Twenty-Faced Symmetrohedron Featuring Four Regular Enneagons, Four Equilateral Triangles, and Twelve Isosceles Triangles

I made this using *Stella 4d*, which you can try for free here.

# A 50-Faced Symmetrohedron Featuring Twelve Regular Hexagons, Six Squares, Eight Equilateral Triangles, and 24 Isosceles Triangles

I made this using *Stella 4d*. You can try this program for free at this website.

# A Symmetrohedron Featuring Twenty Regular Enneagons, Twelve Regular Pentagons, and Sixty Isosceles Triangles

I made this using *Stella 4d: Polyhedron Navigator*. You can get a free trial download of this program at http://www.software3d.com/Stella.php.

# A Symmetrohedron Featuring Six Regular Octagons, Eight Equilateral Triangles, and Twelve Pairs of Isosceles “Bowtie” Trapezoids

This 38-faced polyhedron has been bugging me for over a week. I have a gut feeling that I’ve blogged it before, but my repeated searches have not found it. Perhaps I’m wrong, and it isn’t a “rerun” after all.

I made it using *Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php.

# A Symmetrahedron Featuring Twelve Regular Pentagons

To make this, I stellated the dual of the tetrated dodecahedron over 200 times, and then applied *Stella 4d*‘s “try to make faces regular” function. This is probably not the easiest method to use, but I don’t know of any others. The quadrilaterals are all kites.

If you’d like to give *Stella* a try, for free, the website to visit is http://www.software.com/Stella.php/