Triapeirogonal tiling

Triapeirogonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration(3.)2
Schläfli symbolr{,3} or
Wythoff symbol2 | 3
Coxeter diagram or
Symmetry group[,3], (*32)
DualOrder-3-infinite rhombille tiling
PropertiesVertex-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

The half-symmetry form, , has two colors of triangles:

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

Wikimedia Commons has media related to Uniform tiling 3-i-3-i.


    • 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. 

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