Triapeirogonal tiling

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
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]

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]