# Category Archives: Mathematics

# Four Zonohedra

To build these zonohedra, I used *Stella4d*, a program you may try for free at http://www.software3d.com/Stella.php.

# An Unusual Non-Convex Polyhedron

To make this polyhedron using *Stella 4d*, which you can try for free at http://www.software3d.com/Stella.php, I started with the cuboctahedron. I next dropped the symmetry of the model down from octahedral to tetrahedral, and then I stellated it 54 times.

# Normal and Expanded Versions of the Rhombic Enneacontahedron

The polyhedron above is the rhombic enneacontahedron. Sixty of its faces are wide (yellow) rhombi, while the other thirty are narrow (red) rhombi. The wider rhombi are arranged in twelve panels of five rhombi each. If those panels are moved outward from the center by just the right amount, the narrower rhombi have room to expand, becoming equilateral octagons:

Both of these rotating images were created using *Stella 4d*, a program you can try, for free, at http://www.software3d.com/Stella.php.

# A Polyhedron with 240 Faces, All of Them Quadrilaterals

This polyhedron’s faces are four different types of quadrilaterals. Each type of face appears sixty times. I made it using *Stella 4d: Polyhedron Navigator*, a program you can try out for free at http://www.software3d.com/Stella.php.

# Three Non-convex Polyhedra with Cuboctahedral Symmetry

These were all created using *Stella 4d*, a program you can try — for free — at http://www.software3d.com/Stella.php.

# A Hybrid of the Snub Dodecahedron and the Truncated Icosahedron

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