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In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the
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
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
In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to more ...
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 to542 symmetry
In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1,2 or tr.
Symmetry
There are four small index subgroup constructed from ,4by mirror removal and alternation. In these ...
by adding a bisecting mirror.
Related polyhedra and tiling
References
*John H. Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English people, English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to ...
, 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 geometry, Euclidean, spherical geometry, spherical and hyperbolic geometry, hyperbolic spaces.
The Schläfli symbol describes every regular tessellation of an ' ...
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