Truncated order-8 triangular tiling
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}.
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.
| Type | Reflectional | Rotational |
|---|---|---|
| Index | 1 | 2 |
| Diagram | 
|
|
| Coxeter (orbifold) |
[(4,3,3)] =     (*433) |
[(4,3,3)]+ =   (433) |
Related tilings
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.
See also
- Triangular tiling
- Order-3 octagonal tiling
- Order-8 triangular tiling
- Tilings of regular polygons
- List of uniform tilings
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8.
External links
- Weisstein, Eric W.. "Hyperbolic tiling". http://mathworld.wolfram.com/HyperbolicTiling.html.
- Weisstein, Eric W.. "Poincaré hyperbolic disk". http://mathworld.wolfram.com/PoincareHyperbolicDisk.html.
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
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