Infinite-order triangular tiling: Difference between revisions

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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", seen on the boundary of the [[Poincaré hyperbolic disk]] projection.

== Related polyhedra and tiling ==

This tiling is topologically related as a part of sequence of regular polyhedra with [[Schläfli symbol]] {3,p}.

{{Triangular regular tiling}}

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{{Order i-3 tiling table}}

=== Other infinite-order trianglar tilings===

A nonregular infinite-order trianglar tiling can be generated by a [[Recursion (computer science)|recursive]] process from a central triangle shown here:

:[[File:Ideal-triangle hyperbolic tiling.svg|240px]]

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==References==

{{reflist}}

{{refbegin}}

* [[John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)

* {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}

== External links ==

*{{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}

*{{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}

[[Category:Hyperbolic geometry]]

[[Category:Tessellation]]