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Order-8 square tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic regular tiling: Vertex configuration: 4 8: Schläfli symbol {4,8} Wythoff symbol: 8 | 4 2 Coxeter diagram: Symmetry group [8,4], (*842) Dual: Order-4 octagonal tiling: Properties: Vertex-transitive, edge-transitive, face-transitive
Order-7 square tiling Poincaré disk model of the hyperbolic plane: Type: Hyperbolic regular tiling: Vertex configuration: 4 7: Schläfli symbol {4,7} Wythoff symbol: 7 | 4 2 Coxeter diagram: Symmetry group [7,4], (*742) Dual: Order-4 heptagonal tiling: Properties: Vertex-transitive, edge-transitive, face-transitive
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).
In three-dimensional hyperbolic geometry, the alternated order-6 hexagonal tiling honeycomb is a uniform compact space-filling tessellation (or honeycomb).As an alternation, with Schläfli symbol h{4,3,6} and Coxeter-Dynkin diagram or , it can be considered a quasiregular honeycomb, alternating triangular tilings and tetrahedra around each vertex in a trihexagonal tiling vertex figure.
In geometry, the octagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {8,3} , having three regular octagons around each vertex. It also has a construction as a truncated order-8 square tiling, t{4,8}.
The tetrakis square tiling is the tiling of the Euclidean plane dual to the truncated square tiling. It can be constructed square tiling with each square divided into four isosceles right triangles from the center point, forming an infinite arrangement of lines .
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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