Rhombitriapeirogonal tiling
In geometry, the rhombtriapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of rr{∞,3}.
Symmetry
This tiling has [∞,3], (*∞32) symmetry. There is only one uniform coloring.
Similar to the Euclidean rhombitrihexagonal tiling, by edge-coloring there is a half symmetry form (3*∞) orbifold notation. The apeireogons can be considered as truncated, t{∞} with two types of edges. It has Coxeter diagram 
, Schläfli symbol s2{3,∞}. The squares can be distorted into isosceles trapezoids. In the limit, where the rectangles degenerate into edges, an infinite-order triangular tiling results, constructed as a snub triapeirotrigonal tiling, 
.
Related polyhedra and tiling
Symmetry mutations
This hyperbolic tiling is topologically related as a part of sequence of uniform cantellated polyhedra with vertex configurations (3.4.n.4), 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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