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Examples The hexagonal prism is constructed from both the (6 2 2) and (3 2 2) families.: The truncated square tiling is constructed by two different symmetry positions in the (4 4 2) family.
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 .
The runcitruncated order-4 square tiling honeycomb, t 0,1,3 {4,4,4}, has square tiling, truncated square tiling, cube, and octagonal prism facets, with a square pyramid vertex figure. The runcicantellated order-4 square tiling honeycomb is equivalent to the runcitruncated order-4 square tiling honeycomb.
Truncated order-6 square tiling with *443 symmetry mirror lines The dual tiling represents the fundamental domains of the *443 orbifold symmetry. There are two reflective subgroup kaleidoscopic constructed from [(4,4,3)] by removing one or two of three mirrors.
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
An example of uniform tiling in the Archeological Museum of Seville, Sevilla, Spain: rhombitrihexagonal tiling Regular tilings and their duals drawn by Max Brückner in Vielecke und Vielflache (1900) This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane , and their dual tilings.
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