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Hexagonal tilings can be made with the identical {6,3} topology as the regular tiling (3 hexagons around every vertex). With isohedral faces, there are 13 variations. Symmetry given assumes all faces are the same color. Colors here represent the lattice positions. [2] Single-color (1-tile) lattices are parallelogon hexagons.
This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular and eight semiregular tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type of irregular face.
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
A pattern with this symmetry can be looked upon as a tessellation of the plane with equal triangular tiles with C 3 symmetry, or equivalently, a tessellation of the plane with equal hexagonal tiles with C 6 symmetry (with the edges of the tiles not necessarily part of the pattern).
Sant-Agostino’s Timewood has a geometric pattern of wood-look strips in a cement-look matrix; Provenza’s Alter takes the look of shards and panels of reclaimed oak and blends it seamlessly ...
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