Square tiling
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In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane consisting of four squares around every vertex. John Horton Conway called it a quadrille.
In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane consisting of four squares around every vertex. John Horton Conway called it a quadrille. The square tiling is alternatively formed by the assemblage of infinitely many circles arranged vertically and horizontally, wherein their equal diameter at the center of every point contact with four other circles. Its densest packing is \frac{\pi}{4} \approx 0.785 . There are 3 regular complex apeirogons, sharing the vertices of the square tiling. Regular complex apeirogons have vertices and edges, where edges can contain 2 or more vertices. Regular apeirogons p{q}r are constrained by: 1/p + 2/q + 1/r = 1. Edges have p vertices, and vertex figures are r-gonal.
See also
Tiling with rectangles Fenestrane Langton's ant OpenStructures, design pattern consisting of four squares around every vertex Polyomino
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