Infinite-order triangular tiling: Difference between revisions

Revision as of 03:06, 27 February 2014

Revision as of 09:50, 5 May 2014

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{{Uniform hyperbolic tiles db|Reg hyperbolic tiling stat table|Ui3_2}}

[[File:H3_33inf_UHS_plane_at_infinityH3 33inf UHS plane at infinity.png|thumb|The [[Infinite-order tetrahedral honeycomb|{3,3,∞}]] honeycomb has {3,∞} vertex figures.]]

In [[geometry]], the '''infinite-order triangular tiling''' is a [[regular hyperbolic tiling|regular tiling]] of the [[hyperbolic geometry|hyperbolic plane]] with a [[Schläfli symbol]] of {3,∞}. All vertices are ''ideal'', located at "infinity" and seen on the boundary of the [[Poincaré hyperbolic disk]] projection.

== Symmetry ==

A lower symmetry form has alternating colors, and represented by cyclic symbol {(3,∞,3)}, {{CDD|node_1|split1|branch|labelinfin}}. The tiling also represents the fundamental domains of the [[Iii_symmetryIii symmetry|*∞∞∞ symmetry]], which can be seen with 3 colors of lines representing 3 mirrors of the construction.

{| class=wikitable

|[[File:H2 tiling 33i-4.png|200px]]<BR>Alternated colored tiling

|[[File:Iii_symmetry_mirrorsIii symmetry mirrors.png|200px]]<BR> *∞∞∞ symmetry

|[[File:Apolleangasket_symmetryApolleangasket symmetry.png|200px]]<BR>[[Apollonian gasket]] with *∞∞∞ symmetry

|}

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==See also==

{{CommonscatCommons category|Infinite-order triangular tiling}}

*[[Infinite-order tetrahedral honeycomb]]

*[[List of regular polytopes]]