Tubing Sculpture

For a few years, I’ve been playing with tubing sculptures, like these, with the aim of illustrating symmetries of the hypersphere, described in the final chapter of The Symmetries of Things. Here are some in

Gyring Gyroid

Gyring Gyroid (w Eugene Sargent, 2012, in honor of Tom Rodgers) This piece of samurai space insect armor shows a particular mathematical surface, the gyroid, that naturally arises in many forms. Discovered by Alan Schoen,

A Woven Klein Quartic

Curvature is determined by local geometry, and this can be controlled. A pattern with a particular symmetry is often in an infinite family of patterns, all with the same underlying motif, but of varied curvature

The Pinwheel Tiling

Sometime around 1991, Charles Radin commissioned John Conway for a substitution tiling for which the tiles appeared in infinitely many orientations, and soon John obliged with the Pinwheel. The Pinwheel is formed from right triangles,

Symmetry here and there

All of these photos were taken in 2022, for the upcoming The Magic Theorem of the Symmetries of Things, a second edition of the first part of the book, with expanded exercises and examples, in

A few groovy images

All of these groovy pix use maps from the plane to itself, taking a periodic pattern into the plane in a distorted way. Don’t stare into the middle for too long…

Double Triamond, w/ Hexastix!

“Double Triamond, w/ Hexastix!” created in collaboration with Eugene Sargent, was assembled at the eighth Gathering for Gardner, at Tom Rodgers’ and Sarah Garvin’s beautiful Japanese style gardens and home in Atlanta in 2008. The


You’ll have to cross your eyes or use a stereoscope to see these stereoscopic images, photographed with a stereopi . Tubing and 3D printed connecters are a great way to make models with lots of


The trilobite and cross tiles clearly generalize to higher dimensions. Though a simpler method soon appeared”Threelobites” were a first early graphic / mathematical exploration. Here’s a nice pic of a tiling by the trilobite and