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New Proof of a Strongly Aperiodic Monotile in 3D

Original: A Strongly Aperiodic Monotile in Three Dimensions

Mathematicians have announced a proof of a strongly aperiodic monotile in three dimensions, a single shape that can fill 3D space only in patterns that never repeat periodically. The result extends recent breakthroughs on aperiodic tilings, such as the 2D 'hat' tile discovered in 2023, into a higher-dimensional setting. Readers are discussing the construction methods and what the finding means for the theory of tilings and quasicrystals.

Why now: It extends the celebrated recent aperiodic monotile discoveries into three dimensions, a major result in mathematics.

arXivaperiodic monotilemathematics

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• A Strongly Aperiodic Monotile in Three Dimensions · nhatcher · 4

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