REVIEW 5 cited by
A chiral aperiodic monotile
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original 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.
Forward citations
Cited by 5 Pith papers
-
A $\sigma$-morphic convex protoset
A sigma-morphic protoset made entirely of convex polygons is constructed by replacing the bumps and nicks of a known non-convex example with angular convex notches.
-
On the long-range order of the Spectre tilings
The Spectre tiling and all Spectre-like tilings have pure point diffraction and are MLD to reprojections of a cut-and-project model set, with the smallest possible first Čech cohomology.
-
Quantum error-correcting codes from aperiodic monotiles: the Hat and the Spectre
The Hat and Spectre aperiodic monotiles define erasure-correcting quantum codes with two local-indistinguishability sectors; under SE(2) the Hat retains a superselected chirality bit while the Spectre's label is gauged away.
-
Undecidability of Translational Tiling with Three Tiles
Deciding translational tiling of Z^4 by three connected polyhypercubes is undecidable, shown by reduction from Wang's domino problem.
-
Quasilattices of the Spectre monotile
Decorating every Spectre tile with the same point yields a wide variety of non-periodic quasilattices, including sparse, clustered, and near-hexagonal examples.
Discussion (0). Continue with ORCID to comment.