Toys · WebGL
Chair44
The seven-cube aperiodic monotile, in your browser. Drag to rotate, scroll to zoom, right-drag to pan. Switch between one tile and the 8-, 64- and 512-copy substitution patches, and read the surface features — filled squares are bumps, hollow squares are dents — that force it never to repeat.
Open full screen Best on a desktop with a mouse or trackpad.
Notes
Chair44 is a single solid — a 2×2×2 block of unit cubes with one corner removed — whose 24 exposed faces each carry eight tiny square pyramids. Those bumps and dents are the whole trick: they are the matching rules that let copies fit together in only one way, so the tile fills space without any arrangement ever repeating on a lattice. The viewer draws the exact object from the canonical data; the "schematic" look exaggerates the feature heights so the pattern is visible, and the feature colours are annotations, not part of the solid.
The write-up is in What the 3D Einstein Cannot Erase. Nothing in the viewer is evidence for the theorem; it shows the object the theorem is about.