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  2. 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 ...

  3. List of Euclidean uniform tilings - Wikipedia

    en.wikipedia.org/wiki/List_of_euclidean_uniform...

    This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it. Three dimensional analogues of the planigons are called stereohedrons .

  4. Penrose tiling - Wikipedia

    en.wikipedia.org/wiki/Penrose_tiling

    Concretely, if A S has side lengths (1, 1, φ), then A L has side lengths (φ, φ, 1). B-tiles can be related to such A-tiles in two ways: If B S has the same size as A L then B L is an enlarged version φ A S of A S, with side lengths (φ, φ, φ 2 = 1 + φ) – this decomposes into an A L tile and A S tile joined along a common side of length 1.

  5. Wallpaper group - Wikipedia

    en.wikipedia.org/wiki/Wallpaper_group

    A p4g pattern can be looked upon as a checkerboard pattern of copies of a square tile with 4-fold rotational symmetry, and its mirror image. Alternatively it can be looked upon (by shifting half a tile) as a checkerboard pattern of copies of a horizontally and vertically symmetric tile and its 90° rotated version.

  6. `Like theater in tile form’: Tile’s patterns, designs expand

    www.aol.com/news/theater-tile-form-tile-patterns...

    Tile companies have made great strides in suspending my disbelief that these aren’t actual stone, or other real materials,” says New York-based designer Daniel VanHall. The tech is also ...

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