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  2. Tessellation - Wikipedia

    en.wikipedia.org/wiki/Tessellation

    A tessellation or tiling is the covering of a surface, ... For example, a regular tessellation of the plane with squares has a meeting of four squares at every vertex.

  3. Square tiling - Wikipedia

    en.wikipedia.org/wiki/Square_tiling

    In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning it has 4 squares around every vertex. Conway called it a quadrille. The internal angle of the square is 90 degrees so four squares at a point make a full 360

  4. Pythagorean tiling - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_tiling

    A Pythagorean tiling Street Musicians at the Door, Jacob Ochtervelt, 1665.As observed by Nelsen [1] the floor tiles in this painting are set in the Pythagorean tiling. A Pythagorean tiling or two squares tessellation is a tiling of a Euclidean plane by squares of two different sizes, in which each square touches four squares of the other size on its four sides.

  5. List of tessellations - Wikipedia

    en.wikipedia.org/wiki/List_of_tessellations

    This is a list of tessellations. This list is incomplete; you can help by adding missing items. ... Square tiling: 4 4 {4,4} Triangular tiling: 3 6 {3,6} Hexagonal ...

  6. Euclidean tilings by convex regular polygons - Wikipedia

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

    There must be six equilateral triangles, four squares or three regular hexagons at a vertex, yielding the three regular tessellations. Regular tilings (3) p6m, *632

  7. Cairo pentagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Cairo_pentagonal_tiling

    The snub square tiling is an Archimedean tiling, and as the dual to an Archimedean tiling this form of the Cairo pentagonal tiling is a Catalan tiling or Laves tiling. [14] It is one of two monohedral pentagonal tilings that, when the tiles have unit area, minimizes the perimeter of the tiles.

  8. Cubic honeycomb - Wikipedia

    en.wikipedia.org/wiki/Cubic_honeycomb

    The snub square prismatic honeycomb or simo-square prismatic cellulation is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of cubes and triangular prisms in a ratio of 1:2. It is constructed from a snub square tiling extruded into prisms. It is one of 28 convex uniform honeycombs.

  9. List of regular polytopes - Wikipedia

    en.wikipedia.org/wiki/List_of_regular_polytopes

    The straight apeirogon is a regular tessellation of the line, subdividing it into infinitely many equal segments. It has infinitely many vertices and edges. It has infinitely many vertices and edges. Its Schläfli symbol is {∞}, and Coxeter diagram .