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Truncated order-8 triangular tiling
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In geometry, the truncated order-8 triangular tiling is a semiregular tiling of the hyperbolic plane. There are two hexagons and one octagon on each vertex. It has Schläfli symbol of t{3,8}.
Truncated order-8 triangular tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 8.6.6 |
Schläfli symbol | t{3,8} |
Wythoff symbol | 2 8 | 3 4 3 3 | |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [8,3], (*832) [(4,3,3)], (*433) |
Dual | Octakis octagonal tiling |
Properties | Vertex-transitive |
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Uniform colors
![]() The half symmetry [1+,8,3] = [(4,3,3)] can be shown with alternating two colors of hexagons |
![]() Dual tiling |
Symmetry
The dual of this tiling represents the fundamental domains of *443 symmetry. It only has one subgroup 443, replacing mirrors with gyration points.
This symmetry can be doubled to 832 symmetry by adding a bisecting mirror to the fundamental domain.
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Related tilings
Summarize
Perspective
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling.
It can also be generated from the (4 3 3) hyperbolic tilings:
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (n.6.6), and [n,3] Coxeter group symmetry.
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See also
Wikimedia Commons has media related to Uniform tiling 6-6-8.
References
External links
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