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arXiv:2609.24779math.HO

Notes on a strongly aperiodic monotile in $E^3$

Chaim Goodman-Strauss

Abstract

We provide a clearer presentation of the Chair44 monotile, a new strongly aperiodic monotile in three-dimensional Euclidean space $E^3$.

arXiv comments
10 pages, 6 figures, one model to assemble
Journal reference
DOI
Subjects
math.HOHistory and Overview cs.DMDiscrete Mathematics math.COCombinatorics

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Linked by 2 identifiable commenters in 2 comments across 1 thread, from Oct 2026 to Oct 2026. Found in 1 HN submission from Sep 2026 to Sep 2026. Open submission discussions.

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  1. A Strongly Aperiodic Monotile in Three Dimensions 2 comments

    • See even more: https://arxiv.org/abs/2609.24779

      yorwbaView on HNParent context

    • Yeah, the seven cubes shape tiles R^3 by itself following the aperiodic tiling, but it also tiles R^3 in other ways, some of which are periodic. The bumps prevent any of the periodic tilings. See [1] for a better explanation with a picture of the shape as a rep-tile, and [2] for…

      penteractView on HNParent context

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