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{
    "pk": 64955,
    "title": "A chiral aperiodic monotile",
    "subtitle": null,
    "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 homochiral non-periodic tilings based on a hierarchical substitution system.\n \nMathematics Subject Classifications: 05B45, 52C20, 05B50\n \nKeywords: Tilings, aperiodic order, polyforms",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Tilings"
        },
        {
            "word": "aperiodic order"
        },
        {
            "word": "polyforms"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4xn41982",
    "frozenauthors": [
        {
            "first_name": "David",
            "middle_name": "",
            "last_name": "Smith",
            "name_suffix": "",
            "institution": "Yorkshire, U.K.",
            "department": ""
        },
        {
            "first_name": "Joseph",
            "middle_name": "Samuel",
            "last_name": "Myers",
            "name_suffix": "",
            "institution": "Cambridge, U.K.",
            "department": ""
        },
        {
            "first_name": "Craig",
            "middle_name": "S.",
            "last_name": "Kaplan",
            "name_suffix": "",
            "institution": "School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada",
            "department": ""
        },
        {
            "first_name": "Chaim",
            "middle_name": "",
            "last_name": "Goodman-Strauss",
            "name_suffix": "",
            "institution": "National Museum of Mathematics, New York, New York, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2024-09-26T16:34:05+02:00",
    "date_accepted": "2024-09-26T16:34:05+02:00",
    "date_published": "2024-09-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64955/galley/49765/download/"
        }
    ]
}