"2D Euclidean tilings x3o6o - trat - O2". Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 The Geometrical Foundation of Natural Structure: A Source Book of Design. (Chapter 2.1: Regular and uniform tilings, p. 58-65, Chapter 2.9 Archimedean and Uniform colorings pp. 102–107) Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-8 p. 296, Table II: Regular honeycombs ^ Coxeter, Regular Complex Polytopes, pp.^ Tilings and Patterns, from list of 107 isohedral tilings, p.473-481.^ Order in Space: A design source book, Keith Critchlow, p.74-75, pattern 1.(The truncated triangular tiling is topologically identical to the hexagonal tiling.) Like the uniform polyhedra there are eight uniform tilings that can be based from the regular hexagonal tiling (or the dual triangular tiling).ĭrawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms, 7 which are topologically distinct. Wythoff constructions from hexagonal and triangular tilings It is also topologically related as a part of sequence of Catalan solids with face configuration Vn.6.6, and also continuing into the hyperbolic plane. Symmetry given assumes all faces are the same color. With identical faces ( face-transitivity) and vertex-transitivity, there are 5 variations. The triangular tiling has Schläfli symbol of topology as the regular tiling (6 triangles around every vertex).
Equilateral triangle tessellation esher full#
Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees.
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Tessellations of a plane can be found in the regular patterns of tiles in a bathroom floor, or flagstones in a patio. The regular hexagon is mainly used in the pattern of a honeycomb.
Vertex-transitive, edge-transitive, face-transitive There are only three regular shapes that can even make up a regular tessellation: the equilateral triangle, the square and the regular hexagon. Regular tiling of the plane Triangular tiling
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