Truncated tetraheptagonal tiling

In geometry, the truncated tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of tr{4,7}.

Truncated tetraheptagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration4.8.14
Schläfli symboltr{7,4} or
Wythoff symbol
Coxeter diagram
Symmetry group[7,4], (*742)
DualOrder-4-7 kisrhombille tiling
PropertiesVertex-transitive

Images

Poincaré disk projection, centered on 14-gon:

Symmetry
Truncated tetraheptagonal tiling with mirror lines.

The dual to this tiling represents the fundamental domains of [7,4] (*742) symmetry. There are 3 small index subgroups constructed from [7,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.

References
  • 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.

See also
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