Infinite-order triangular tiling: Difference between revisions

Revision as of 04:49, 29 May 2018

Revision as of 18:27, 28 March 2021

Line 1:

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

[[File:H3 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 symmetry|*∞∞∞∞∞∞ symmetry]], which can be seen with 3 colors of lines representing 3 mirrors of the construction.

{| class=wikitable width=450

|- align=center