Rhombitriapeirogonal tiling

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Rhombitriapeirogonal tiling
Rhombitriapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.4.∞.4
Schläfli symbol rr{∞,3} or
s2{3,∞}
Wythoff symbol 3 | ∞ 2
Coxeter diagram CDel node 1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png or CDel node.pngCDel split1-i3.pngCDel nodes 11.png
CDel node 1.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png
Symmetry group [∞,3], (*∞32)
[∞,3+], (3*∞)
Dual Deltoidal triapeirogonal tiling
Properties Vertex-transitive

In geometry, the rhombtriapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of rr{∞,3}.

Symmetry[edit]

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 CDel node h.pngCDel 3.pngCDel node h.pngCDel infin.pngCDel node 1.png, 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 an snub triapeirotrigonal tiling, CDel node h.pngCDel 3.pngCDel node h.pngCDel infin.pngCDel node.png.

Related polyhedra and tiling[edit]

Symmetry mutations[edit]

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[edit]

References[edit]

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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. 

External links[edit]