Periodic diffraction from an aperiodic monohedral tiling - the Spectre tiling. Addendum

Acta Crystallogr A Found Adv. 2024 Nov 1;80(Pt 6):460-463. doi: 10.1107/S2053273324008945. Epub 2024 Oct 8.

Abstract

This article describes the diffraction pattern (2-periodic Fourier transform) from the vertices of a large patch of the recently discovered `Spectre' tiling - a strictly chiral aperiodic monotile. It was reported recently that the diffraction pattern of the related weakly chiral aperiodic `Hat' monotile was 2-periodic with chiral plane-group symmetry p6 [Kaplan et al. (2024). Acta Cryst. A80, 72-78]. The diffraction periodicity arises because the Hat tiling is a systematic aperiodic deletion of vertices from the 2-periodic hexagonal mta tiling. Despite the similarity of the Hat and Spectre tilings, the Spectre tiling is not aligned with a 2-periodic lattice, and its diffraction pattern is non-periodic with chiral point symmetry 6 about the origin.

Keywords: Hat tiling; Spectre tiling; aperiodic monotiling.

Publication types

  • Published Erratum