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  2. List of Euclidean uniform tilings - Wikipedia

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

    The Laves tilings have vertices at the centers of the regular polygons, and edges connecting centers of regular polygons that share an edge. The tiles of the Laves tilings are called planigons. This includes the 3 regular tiles (triangle, square and hexagon) and 8 irregular ones. [4] Each vertex has edges evenly spaced around it.

  3. Hexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_tiling

    In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t {3,6} (as a truncated triangular tiling).

  4. Euclidean tilings by convex regular polygons - Wikipedia

    en.wikipedia.org/wiki/Euclidean_tilings_by...

    For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...

  5. Trihexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Trihexagonal_tiling

    The trihexagonal tiling has Schläfli symbol of r{6,3}, or Coxeter diagram, , symbolizing the fact that it is a rectified hexagonal tiling, {6,3}. Its symmetries can be described by the wallpaper group p6mm, (*632), [15] and the tiling can be derived as a Wythoff construction within the reflectional fundamental domains of this group.

  6. Cairo pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Cairo_pentagonal_tiling

    The six coordinates of each pentagon can be grouped into two triples of coordinates, in which each triple gives the coordinates of a hexagon in an analogous three-dimensional coordinate system for each of the two overlaid hexagon tilings. [10] The number of tiles that are steps away from any given tile, for =,,, …, is given by the ...

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