Editing Hyperbolic geometry (section)

=== Tessellations ===
{{main article|Uniform tilings in hyperbolic plane}}
{{see also|Regular hyperbolic tiling}}

[[File:Rhombitriheptagonal tiling.svg|thumb|[[Rhombitriheptagonal tiling]] of the hyperbolic plane, seen in the [[Poincaré disk model]] ]]
Like the Euclidean plane it is also possible to tessellate the hyperbolic plane with [[regular polygon]]s as [[Face (geometry)|faces]].

There are an infinite number of uniform tilings based on the [[Schwarz triangles]] (''p'' ''q'' ''r'') where 1/''p'' + 1/''q'' + 1/''r'' < 1, where ''p'',&thinsp;''q'',&thinsp;''r'' are each orders of reflection symmetry at three points of the [[fundamental domain triangle]], the symmetry group is a hyperbolic [[triangle group]]. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles, some for example requiring quadrilaterals as fundamental domains.<ref>{{Cite journal | doi=10.1140/epjb/e2003-00032-8|title = Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings| journal=The European Physical Journal B | volume=31| issue=2| pages=273–284|year = 2003|last1 = Hyde|first1 = S.T.| last2=Ramsden| first2=S.|bibcode = 2003EPJB...31..273H| citeseerx=10.1.1.720.5527|s2cid = 41146796}}</ref>