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Truncated order-4 heptagonal tiling
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In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.
Truncated heptagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic uniform tiling |
Vertex configuration | 4.14.14 |
Schläfli symbol | t{7,4} |
Wythoff symbol | 2 4 | 7 2 7 7 | |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [7,4], (*742) [7,7], (*772) |
Dual | Order-7 tetrakis square tiling |
Properties | Vertex-transitive |
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Constructions
There are two uniform constructions of this tiling, first by the [7,4] kaleidoscope, and second by removing the last mirror, [7,4,1+], gives [7,7], (*772).
Symmetry
There is only one simple subgroup [7,7]+, index 2, removing all the mirrors. This symmetry can be doubled to 742 symmetry by adding a bisecting mirror.
Related polyhedra and tiling
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.
See also
Wikimedia Commons has media related to Uniform tiling 4-14-14.
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- 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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