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The square tiling has 9 uniform colorings: 1111, 1112(a), 1112(b), 1122, 1123(a), 1123(b), 1212, 1213, 1234. In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive.
Geometric discrepancy theory [1] is a sub-field of discrepancy theory, that deals with balancing geometric sets, such as intervals or rectangles.The general research question in this field is: given a set of points in a geometric space, and a set of objects in the same space, can we color each point in one of two different colors (e.g. black and white), such that each object contains roughly ...
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
There is only one uniform coloring. Similar to the Euclidean rhombitrihexagonal tiling, by edge-coloring there is a half symmetry form (3*4) orbifold notation. The octagons can be considered as truncated squares, t{4} with two types of edges. It has Coxeter diagram, Schläfli symbol s 2 {3,8}. The squares can be distorted into isosceles trapezoids.
Order-7 square tiling: Properties: ... This coloring represents the uniform tiling t 1 {7,7} ... The Beauty of Geometry: Twelve Essays. Dover Publications. 1999.
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John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations) "Chapter 10: Regular honeycombs in hyperbolic space".
In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There is one square , one hexagon , and one tetradecagon (14-sides) on each vertex . It has Schläfli symbol of tr{7,3}.
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