Truncated infinite-order triangular tiling
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In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{3,∞}.
Symmetry
The dual of this tiling represents the fundamental domains of *∞33 symmetry. There are no mirror removal subgroups of [(∞,3,3)], but this symmetry group can be doubled to ∞32 symmetry by adding a mirror.
| Type | Reflectional | Rotational |
|---|---|---|
| Index | 1 | 2 |
| Diagram | 
|
|
| Coxeter (orbifold) |
[(∞,3,3)]    (*∞33) |
[(∞,3,3)]+  (∞33) |
Related polyhedra and tiling
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (6.n.n), and [n,3] Coxeter group symmetry.
See also
- List of uniform planar tilings
- Tilings of regular polygons
- Uniform tilings in hyperbolic plane
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.
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