Counting matching models…
Take the configuration of the sticks of 12 Sticks , the Mirii 4x3 , or Coubion . Let the sticks repel each other while maintaining the octahedral symmetry . Stop when the nearest six rods are equally far away. Equivalently, you can also…
Caution: Sink the model so the first layer is not empty! The moving sofa problem asks for the largest sofa that can pass a hallway with a right angle turn. In 1968, Hammersley proposed this shape defined by segments and arcs with area…
Take a cube. Rotate each edge by 54.7356103172 degrees. Congratulations, you get the skeleton of the famous Hexsticks / Hectix / Tetraxis puzzle. Compute the contour of the equation D ( x , 1st-edge)⁻¹⁰ = r ⁻¹⁰ + D ( x , 2nd-edge)⁻¹⁰+ D (…
Take the configuration of the rods of the famous Nova Plexus . Let the rods repel each other while maintaining the tetrahedral symmetry . Stop when the nearest five rods are equally far away. Congraduations, you rediscover the Tetra Cage…
This is inspired by @wafflecart's But instead of squares of sizes 1 and 2, I want to use squares of different sizes to form a rectangle. This is called a squared rectangle . The following is the smallest design found on the internet. i i…
You have seen Dudeney's hinged triangle that swings into a square. But do you know that I, O, T, S, Z, L, and J pieces can be formed by one hinged structure? Taken from David Eppstein's website , this is the print-in-place version of the…
Here are some QR codes that seem to connect you to Wi-Fi, but they're all Rickrolls. Some are harder to scan (I had to break more rules of the QR standard to honor the pixel art), so test-scan before you print. Each QR code points to a…
Thanks to David Ellsworth's high-precision SVGs , I turned them into 3D models for potential creative uses. Some discussion that went through my head: Make a big square tray with separate cubes to pack inside. Too easy to knock everything…
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