Stereopix
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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 circles, and perfect for stereoscopic images of great circles in the hypersphere. Here are illustrations of a few of discrete symmetries of the hypersphere (Tables 26.1, 26.2 and 26.3 of the Symmetries of Things) — I have many more of these models that I need to photograph. Really though, they would like to be 14′ tall in powder coated aluminum!
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The compound of three hypercubes, or a coloring of the edges of the 24-cell, with symmetry ±1/6 [OxO].
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Ultimately, to fully illustrate these symmetries, the plan/dream is to make larger scale sculptures using programmable LEDs within wider diameter tubing. A test piece hung on our porch for about a year, with dynamic glowing colors illustrating subgroups of ±[TxT] (as per the tables). Meanwhile, here are two more subgroups of the more complicated ±[OxO] — the wiring defeated my LED ambitions for the time being.
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In the background is a model of made of cubes, that can be extended to fill all space, using a simple rule — the cubes each meet four others, gyrorotationally (with local symmetry 2X). The infinite model would have the mysterious quarter group symmetry, 8o:2 , #229 Intl No. The quarter groups, all sub symmetries of this one, are not easy to visualize, and there will be a post just on the various models and sculptures I’ve produced to illustrate these as best I can. Many of those were suggested by Conway, who himself was fascinated and beguiled by these strange space symmetries.
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Here is another interesting quarter group symmetry, one of many possible using this system of injection molded pieces, forming a coloring of the triamond or Laves lattice. This system will show up in another post, but these are the only stereoscopic pix I took.
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Here are some older experiments:
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tetrastix:
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The mu-snub cube, a form that relaxes to the gyroid:
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