2023/05/28 by David Smith, David J. Smith, Joseph Samuel Myers +2 · 5 voices · 6 citations
Materials Science · Computer Science · Engineering · #Quasicrystal Structures and Properties #Matrix Theory and Algorithms #Advanced Materials and Mechanics
paper · pdf · doi:10.5070/c64264241
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 homochiral non-periodic tilings based on a hierarchical substitution system.Mathematics Subject Classifications: 05B45, 52C20, 05B50Keywords: Tilings, aperiodic order, polyforms