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- W4378767302 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." @default.
- W4378767302 created "2023-05-31" @default.
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- W4378767302 date "2023-05-28" @default.
- W4378767302 modified "2023-10-16" @default.
- W4378767302 title "A chiral aperiodic monotile" @default.
- W4378767302 doi "https://doi.org/10.48550/arxiv.2305.17743" @default.
- W4378767302 hasPublicationYear "2023" @default.
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