Tag Archive for Tiling



Tessellation is “a collection of shapes [tiles] that fit together without gaps or overlap to cover the infinite mathematical plane” (Fathauer, 2021). Most tilings are “periodic,” in the sense that the pattern repeats itself when “translated” (shifted without rotation). In the 1970s Roger Penrose described several sets of tiles that could cover the plane aperiodically. The search then began for the “einstein” (one stone) – a single tile that could cover the plane aperiodically. In March of 2023, Smith, Myers, Kaplan & Goodman-Strauss described a tile, commonly known as the “hat” that covered the plane aperiodically. However, to do so, this tile had to be occasionally turned over (to make its mirror image). Subsequently in May of 2023, the same authors reported another tile that could cover the plane aperiodically without any need for mirror images. This tile was called the “spectre.” This posting briefly reviews these recent developments in a style more visual than verbal.

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