alternated order-4 hexagonal tiling
{{Short description|Uniform tiling of the hyperbolic plane}}
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U443_0}}
In geometry, the alternated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of (3,4,4), h{6,4}, and hr{6,6}.
Uniform constructions
There are four uniform constructions, with some of lower ones which can be seen with two colors of triangles:
| class=wikitable
! *443 ! 3333 ! *3232 ! 3*22 |
| align=center
| {{CDD|node_h1|6|node|4|node}} = {{CDD|branch_10ru|split2-44|node}} | {{CDD|node_h|6|node_g|4sg|node_g}} = {{CDD|branch_hh|3a3b-cross|branch_hh}} | {{CDD|node_h1|6|node|4|node_h0}} = {{CDD|node_h1|split1-66|nodes}} = {{CDD|nodes_11|3a3b-cross|nodes}} | {{CDD|node_h|6|node_h0|4|node}} = {{CDD|branch_hh|2a2b-cross|nodes}} |
| align=center
|colspan=2|120px |colspan=2|120px |
| colspan=2|(4,4,3) = h{6,4}
!colspan=2|hr{6,6} = h{6,4}{{frac|1|2}} |
|---|
Related polyhedra and tiling
{{Order 6-4 tiling table}}
{{Order 6-6 tiling table}}
{{Order 4-4-3 tiling table}}
{{Order 3-2-3-2 tiling table}}
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)
- {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}
See also
{{Commonscat|Uniform tiling 3-4-3-4-3-4-3-4}}
External links
- {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
- {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
- [http://bork.hampshire.edu/~bernie/hyper/ Hyperbolic and Spherical Tiling Gallery] {{Webarchive|url=https://web.archive.org/web/20130324095520/http://bork.hampshire.edu/~bernie/hyper/ |date=2013-03-24 }}
- [http://geometrygames.org/KaleidoTile/index.html KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings]
- [http://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch]
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