Strongly aperiodic tile discovered that fills 3d space uniquely
Notes on a strongly aperiodic monotile in $E^3$
Discrete Mathematics
Summary
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.
What this means in practice
- •For 3d printing designers: Design complex non-repeating 3D structures using Chair44 tile arrangements for architectural or artistic models.
- •For crystallography researchers: Use the Chair44 monotile to model or analyze materials with non-repetitive atomic structures and symmetry properties.
Authors
Chaim Goodman-Strauss
Abstract
We provide a clearer presentation of the Chair44 monotile, a new strongly aperiodic monotile in three-dimensional Euclidean space $E^3$.