Truncated octagonal tiling
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| Truncated octagonal tiling | |
|---|---|
| Truncated octagonal tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.16.16 |
| Schläfli symbol | t{8,3} |
| Wythoff symbol | 2 3 | 8 |
| Coxeter diagram | File:CDel node 1.pngFile:CDel 8.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.png |
| Symmetry group | [8,3], (*832) |
| Dual | Order-8 triakis triangular tiling |
| Properties | Vertex-transitive |
In geometry, the truncated octagonal tiling is a semiregular tiling of the hyperbolic plane. There is one triangle and two hexakaidecagons on each vertex. It has Schläfli symbol of t{8,3}.
Dual tiling
The dual tiling has face configuration V3.16.16.
Related polyhedra and tilings
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
See also
Wikimedia Commons has media related to Uniform tiling 3-16-16.
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. LCCN 99035678.
