@mananself
Joined July 2009
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The U.S. flag packs 50 stars into a rectangle. I found a packing with stars 95% larger in diameter. It has central symmetry and is our best so far, though not proven optimal. I don't know if an optimal packing has central symmetry. AI-assisted search.
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Last night I had a dream: I worked on a wireless communication problem with many antennas. The output at the i-th antenna was y_i=f_i(inputs). The problem is therefore named y_i,f_i, and pronounced WiFi.
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I built a non-coplanar physical Zometool approximation of the aperiodic Spectre tiling. Zometool cannot make 30-degree angles exactly, so this uses red/blue struts at about 31.7 degrees. The even/odd tile classes show up as a red/blue swap. Spot the odd one out?
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Follow-up xitter.cf/mananself/status/20376… out of 43380 dodecahedron nets, exactly 74 also fold into the great dodecahedron (with faces passing through each other). That's fewer than 1 in 500. All 74 nets: github.com/nanma80/star-poly…
Nan Ma@mananselfMar 27
I built a paper model of a great dodecahedron from 12 pentagonal "flower" shapes. This net has a rare dual property: it also folds into a regular dodecahedron. Folding the great dodecahedron requires weaving the faces through each other: messy in the middle, satisfying at the end
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I built a paper model of a great dodecahedron from 12 pentagonal "flower" shapes. This net has a rare dual property: it also folds into a regular dodecahedron. Folding the great dodecahedron requires weaving the faces through each other: messy in the middle, satisfying at the end
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I made Lights Out 4D: the classic puzzle game, but on 4D polytopes. Click vertices to toggle rings. Turn them all off to win. Three shapes: 16-cell, 24-cell, 600-cell. Works on phone & desktop. nan.ma/lights_out_4d/
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Still playing with the yellow Cairo tiles from my last post. Six tiles form a ring with a regular hexagon in the center. Fill it with a white hex tile and it becomes a flower; leave it open and it's a hollow hexagon. These larger hexagons can tile the plane.
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Links to the previous posts for these two tiles: xitter.cf/mananself/status/20250… xitter.cf/mananself/status/19263…
Nan Ma@mananself24 May 2025
My latest coordinated-motion model is flat and based on a hexagonal tiling, with all the identical pieces moving in and out simultaneously. The mechanism is the same as in the classic Magic Disc and my Blast-hedra puzzles. I can make as many pieces as I like this time.
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I built a 2D coordinate-motion model based on the periodic Cairo tiling. Identical pieces move in and out together. There are two expanding motions, rotated 90° from each other — each opens half the triangular holes. Combined, they open all the holes uniformly.
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Various stages of the motions
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Two puzzles I'm building: 🔴 12 pieces slide into a cube with coordinated motions in 2D abstract space. 🔵 30 pieces form a dodecahedron with 4D motions. Inspired by John Kostick's designs. john-kostick.github.io/vzome…
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More pictures:
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My latest coordinated-motion model is flat and based on a hexagonal tiling, with all the identical pieces moving in and out simultaneously. The mechanism is the same as in the classic Magic Disc and my Blast-hedra puzzles. I can make as many pieces as I like this time.
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My latest coordinate-motion model with 20 pieces, based on the compound of five tetrahedra. We can assemble the 20 identical pieces into five separate tetrahedra or into one large ball.
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Assembling 12 identical pieces with coordinated motion simultaneously to form a soccer ball shape. It requires aligning all 12 pieces and move them inwards at the same time. I made two simpler models with 4 and 6 pieces. You may buy them here: nothingyetdesigns.com/collec…
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Recently I designed and 3d printed a coordinated-motion model. There are 4 identical pieces. When we assemble them, all pieces move simultaneously towards the center to form an octahedron. Then I spin it to disassemble.
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The AI roast bot took a long time to process my profile, and it finally came back. I'm very flattered to hear that I'm a human embodiment of a Rubik's Cube, hopefully it's the 4D version.
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I improved my model of 30 pencils using colorful pencils. Now 5 pencils in each bundle have the same color, with 6 colors in total. @standupmaths if you can get the pencil manufacturer to make pentagonal pencils with 6 colors, you may make the ideal model.
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Previously I made two pencil models, each with 30 pencils. John Kostick suggested that they can be combined together, because one fits into the gap of the other. Now I have a model with 60 pencils with the icosahedral symmetry.
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The new model has 6 bundles of 5 pencils, plus 10 bundles of 3 pencils. The rubber bands are binding the bundles.
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