Convex Uniform Tilings of The Euclidean Plane
All reflectional forms can be made by Wythoff constructions, represented by Wythoff symbols, or Coxeter-Dynkin diagrams, each operating upon one of three Schwarz triangle (4,4,2), (6,3,2), or (3,3,3), with symmetry represented by Coxeter groups:, or ]. Alternated forms such as the snub can also be represented by special markups within each system. Only one uniform tiling can't be constructed by a Wythoff process, but can be made by an elongation of the triangular tiling. An orthogonal mirror construction also exists, seen as 2 sets of parallel mirrors making a rectangular fundamental domain. If the domain is square, this symmetry can be doubled by a diagonal mirror into the family.
Families:
- (4,4,2), - Symmetry of the regular square tiling
- ,
- (6,3,2), - Symmetry of the regular hexagonal tiling and triangular tiling.
- (3,3,3), ]
Read more about this topic: List Of Uniform Tilings
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