AI Helps Discover a 3D Tile That Never Repeats
A new three-dimensional shape called Chair44 can fill space completely without gaps or overlaps and without ever repeating its pattern. It follows the 2023 discovery of a two-dimensional 'hat' tile that also tiles aperiodically. The preprint's sole human author used an AI model to help find the shape.
The 2023 hat tile was found by amateur David Smith and later proven aperiodic with Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss in Combinatorial Theory. "Einstein" derives from German for "one shape." Chair44 carries this search into 3D.
Ioannis Tsiokos, who directs Automorph, is the preprint's only human author. He used Claude Fable 5.1 to draft the manuscript and ChatGPT-6 Astra to locate and check the monotile. Kaplan notes the older Schmitt-Conway-Danzer biprism is only weakly aperiodic; Chair44 offers a robust case.
The discovery may energize tiling theory and geometry outreach, potentially drawing students and hobbyists toward mathematical play. AI-assisted research could affect how mathematicians, scientists, and software tools collaborate, perhaps speeding searches for complex structures while raising questions about verification and authorship. Designers, materials scientists, and computer graphics researchers might explore aperiodic 3D tilings for novel patterns or structures, though practical applications remain speculative.