A 13-sided polykite — the hat — that tiles the plane but never periodically. The first aperiodic monotile; Spectre later dropped the reflections.
Smith, Myers, Kaplan & Goodman-Strauss, 2023
David Smith found the 13-sided hat in 2023; Myers, Kaplan, and Goodman-Strauss proved it is an aperiodic monotile — one shape, no periodic tiling, reflections allowed. The Spectre, later that year, tiles without mirrors.
tiling
MonotileThirteen sides, one tile. Copy it, reflect it, and the plane fills — never periodically.