Hugging Peers

A chiral aperiodic monotile

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David Smith,Joseph Samuel Myers,Craig S. Kaplan,Chaim Goodman-Strauss
Combinatorial Theory, 4(2) (2024) cs.DMmath.COmath.MG
23 citations published

Abstract

The recently discovered "hat" aperiodic monotile mixes unreflected and reflected tiles in every tiling it admits, leaving open the question of whether a single shape can tile aperiodically using translations and rotations alone. We show that a close relative of the hat -- the equilateral member of the continuum to which it belongs -- is a weakly chiral aperiodic monotile: it admits only non-periodic tilings if we forbid reflections by fiat. Furthermore, by modifying this polygon's edges we obtain a family of shapes called Spectres that are strictly chiral aperiodic monotiles: they admit only chiral non-periodic tilings based on a hierarchical substitution system.

Cite this paper

@article{smith2023,
  title = {A chiral aperiodic monotile},
  author = {David Smith and Joseph Samuel Myers and Craig S. Kaplan and Chaim Goodman-Strauss},
  journal = {Combinatorial Theory, 4(2) (2024)},
  year = {2023},
  month = {May},
  doi = {10.5070/c64264241},
  url = {https://doi.org/10.5070/c64264241},
}