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  2. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

    en.wikipedia.org/wiki/Lists_of_uniform_tilings...

    Right triangle domains can have as few as 1 face type, making regular forms, while general triangles have at least 2 triangle types, leading at best to a quasiregular tiling. There are different notations for expressing these uniform solutions, Wythoff symbol , Coxeter diagram , and Coxeter's t-notation.

  3. List of aperiodic sets of tiles - Wikipedia

    en.wikipedia.org/.../List_of_aperiodic_sets_of_tiles

    Smallest aperiodic set of Wang tiles. No image: Decagonal Sponge tile: 1: E 2: 2002 [58] [59] Porous tile consisting of non-overlapping point sets. No image: Goodman-Strauss strongly aperiodic tiles: 85: H 2: 2005 [60] No image: Goodman-Strauss strongly aperiodic tiles: 26: H 2: 2005 [61] Böröczky hyperbolic tile: 1: H n: 1974 [62] [63] [61 ...

  4. Shower (juggling) - Wikipedia

    en.wikipedia.org/wiki/Shower_(juggling)

    "In the shower pattern, every ball is thrown in a high arc from the right hand to the left (or vice versa) and then quickly passed off with a low throw from the left to the right hand (or vice versa)." [3] The animation depicts a 3-ball version. Siteswap notation for shower patterns is (2n-1)1, where n is the number of objects juggled. (i.e. 31 ...

  5. Pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Pentagonal_tiling

    There are also 2-isohedral tilings by special cases of type 1, type 2, and type 4 tiles, and 3-isohedral tilings, all edge-to-edge, by special cases of type 1 tiles. There is no upper bound on k for k-isohedral tilings by certain tiles that are both type 1 and type 2, and hence neither on the number of tiles in a primitive unit.

  6. Einstein problem - Wikipedia

    en.wikipedia.org/wiki/Einstein_problem

    Tile(1,1) from Smith, Myers, Kaplan & Goodmann-Strauss on the left. A spectre is obtained by modifying the edges of this polygon as in the middle and right example. In May 2023 the same team (Smith, Myers, Kaplan, and Goodman-Strauss) posted a new preprint about a family of shapes, called "spectres" and related to the "hat", each of which can ...

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