truncated order-4 pentagonal tiling
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In
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
, the truncated order-4 pentagonal tiling is a uniform tiling of the
hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P' ...
. It has Schläfli symbol of t0,1.


Uniform colorings

A half symmetry +,4,5= ,5coloring can be constructed with two colors of decagons. This coloring is called a ''truncated pentapentagonal tiling''. :


Symmetry

There is only one subgroup of ,5 ,5sup>+, removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror.


Related polyhedra and tiling


References

* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations) *


See also

*
Uniform tilings in hyperbolic plane In hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive ( transitive on its v ...
*
List of regular polytopes This article lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ''n''-sphere, Euclidean and hyperbolic spaces. A Schläfli ...


External links

* *
Hyperbolic and Spherical Tiling Gallery


* ttp://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch Hyperbolic tilings Isogonal tilings Order-4 tilings Pentagonal tilings Truncated tilings Uniform tilings {{geometry-stub