Tetraheptagonal tiling

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

Tetraheptagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration(4.7)2
Schläfli symbolr{7,4} or
rr{7,7}
Wythoff symbol7 4
7 7 | 2
Coxeter diagram
Symmetry group[7,4], (*742)
[7,7], (*772)
DualOrder-7-4 rhombille tiling
PropertiesVertex-transitive edge-transitive

Symmetry


A half symmetry [1+,4,7] = [7,7] construction exists, which can be seen as two colors of heptagons. This coloring can be called a rhombiheptaheptagonal tiling.

The dual tiling is made of rhombic faces and has a face configuration V4.7.4.7.

See also

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.
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