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 stereo, and below are many others. To be fair, these are impossible to understand without holding in your hand — or better yet, climbing through big ones!

These sculptures illustrate symmetries of the hypersphere, which projects nicely into our space by stereographic projection, taking circles to circles (possibly of infinite radius). All of these arcs are on perfect circles (if the models were perfect) — hence tubing, with a built in curvature, is a suitable material.

The aim is to make these larger, lit up with programmable LEDs, as interactive light organs — a single system of edges can illustrate many different symmetries by the way it is lit.

For more than a year, we had a LED sculpture on our front porch, simpler than these but impressive enough as it went through its routines. Somehow I never really documented it, though lots of passersby sure did:

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