3d aperiodic monotile: chair44
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A new version, also based on Goodman-Strauss's arrow markings. (No guarantee it fits, or is indeed aperiodic.)
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Chair44 — Experimental Geometric Relief
A geometric relief model based on Chaim Goodman–Strauss’s Chair44 arrow markings. The markings are represented by tetrahedral bumps and dents. Where neighboring dents meet, their shared internal walls are removed to form joined cavities.
The model is 48 millimeters across and has 98 planar faces. The STL and 3MF contain the same verified watertight solid. The included OpenSCAD source allows uniform resizing. The images and rotating GIF are computer renders, not photographs of a finished print.
Printing notes
This model has not yet been physically test-printed. It includes undercuts and pointed protrusions, so review the orientation and supports in your slicer. No fitting clearance has been added. Start with two copies to check real-world tolerances before printing a larger set. Printer and material settings have not been validated.
Assembly notes
Computer checks confirm that the mating pairs in the first eight-tile supertile can slide together when tested as two copies. Assembling all eight requires coordinated motion; one-at-a-time straight sliding does not complete it.
At the next level, rigid eight-tile supertiles cannot be assembled by translation alone. Rotation-assisted assembly remains untested. Aperiodicity of this particular unmarked relief solid has not been established.
Credits and references
Mathematical construction and arrow markings: Chaim Goodman–Strauss https://arxiv.org/abs/2609.24779
A similar version by Pieter Mostert https://editor.p5js.org/pieter_mostert/full/oPvZLHNm9
Interactive model: https://liuyao12.github.io/geometric-tree-search/3d-reptiles/
CAD generation, rendering, and computational verification were AI-assisted.