Newly discovered 3D 'chair' shape can fill all space without repeating patterns
A software developer has discovered a 3D aperiodic monotile, a shape that can fill space infinitely without repeating its pattern. This breakthrough, assisted by AI, solves a long-standing mathematical challenge regarding shapes that lack global symmetry.
Why it matters
This discovery provides a significant advancement in geometry and tiling theory, with potential applications in materials science and structural design.
edited by Gaby Clark , reviewed by Robert Egan
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Add to Preferred Sources The solid Q , with feature bases enlarged × 5 and signed heights × 80 for visibility. Credit: arXiv (2026). DOI: 10.48550/arxiv.2609.19214 Software developer Ioannis Tsiokos has reported the discovery of a three-dimensional shape, which roughly resembles a chair, that can fill space infinitely without repeating a pattern. The shape follows certain mathematical rules that make it the first of its kind in three dimensions. The AI-assisted findings are described in an arXiv preprint paper .
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