Triapeirogonal tiling

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Triapeirogonal tiling
Triapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (3.∞)2
Schläfli symbol r{∞,3} or
Wythoff symbol 2 | ∞ 3
Coxeter diagram CDel node.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node.png or CDel node 1.pngCDel split1-i3.pngCDel nodes.png
CDel labelinfin.pngCDel branch 11.pngCDel split2.pngCDel node.png
Symmetry group [∞,3], (*∞32)
Dual Order-3-infinite rhombille tiling
Properties Vertex-transitive edge-transitive

In geometry, the triapeirogonal tiling (or trigonal-horocyclic tiling) is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,3}.

Uniform colorings[edit]

The half-symmetry form, CDel labelinfin.pngCDel branch 11.pngCDel split2.pngCDel node.png, has two colors of triangles:

H2 tiling 33i-3.png

Related polyhedra and tiling[edit]

This hyperbolic tiling is topologically related as a part of sequence of uniform quasiregular polyhedra with vertex configurations (3.n.3.n), and [n,3] Coxeter group symmetry.

See also[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]