Papers for

crystallography researchers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Strongly aperiodic tile discovered that fills 3d space uniquely

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

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

Mon 21 SeptDiscrete Mathematics
The gist
The paper explains a special kind of three-dimensional tile called Chair44 that can fill space without repeating patterns. This tile is unique because it forces arrangements with no periodic repetition, unlike many regular shapes. The authors provide a clearer explanation of this tile and how it works in 3D space. This helps understand how complex, non-repeating patterns can form from a single shape.
Open → 2609.24779v1