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The Geometiles Klein Bottle

Delighting mathematicians, artists, and children alike, the Klein Bottle is a whimsical and perplexing surface that was discovered by the German mathematician Felix Klein in late 19th century. While it is most frequently seen visiting our three dimensional world in the form below, its true home is 4 dimensional space; there it fits comfortably, without…
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Pi Day 2022: a regular 30 sided polygon.

Several years ago, I explored approximating Pi with polygons made of Geometiles. I described my findings in this blog. Fast forward to 2022, when Charles Fleischer showed me a polyhedral torus I’ve never seen before, and its boundary was a regular 30-sided polygon. The fancy name for a 30 sided polygon is triacontagon. Triaconta τριάκοντα…
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Campanus’ Sphere

In these very uncertain times, I find it comforting to look at something eternal and classical. It’s even better if this is an object whose model I can construct. After months of quarantine, I finally hit upon the perfect pandemic craft object: the Campanus’ Sphere. This beautiful polyhedral frame was frequently portrayed during the Rennaissance…
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