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Truncated tetrapentagonal tiling

A uniform tiling of the hyperbolic plane From Wikipedia, the free encyclopedia

Truncated tetrapentagonal tiling
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In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1,2{4,5} or tr{4,5}.

Truncated tetrapentagonal tiling
Thumb
Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration4.8.10
Schläfli symboltr{5,4} or
Wythoff symbol2 5 4 |
Coxeter diagram or
Symmetry group[5,4], (*542)
DualOrder-4-5 kisrhombille tiling
PropertiesVertex-transitive
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Symmetry

Thumb
Truncated tetrapentagonal tiling with mirror lines.

There are four small index subgroup constructed from [5,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.

A radical subgroup is constructed [5*,4], index 10, as [5+,4], (5*2) with gyration points removed, becoming orbifold (*22222), and its direct subgroup [5*,4]+, index 20, becomes orbifold (22222).

More information Small index subgroups of [5,4], Index ...
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More information Symmetry*n42 [n,4], Spherical ...
More information Symmetry*nn2 [n,n], Spherical ...
More information Symmetry: [5,4], (*542), [5,4]+, (542) ...
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See also

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • Coxeter, H. S. M. (1999). "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. ISBN 0-486-40919-8. LCCN 99035678.


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