Non-Euclidean crystallographic group
This article is about the mathematical concept. For the British state-owned venue management company, see NEC Group.
In mathematics, a non-Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry. A NEC group which contains only orientation-preserving elements is called a Fuchsian group, and any non-Fuchsian NEC group has an index 2 Fuchsian subgroup of orientation-preserving elements.
The hyperbolic triangle groups are notable NEC groups. Others are listed in Orbifold notation here.
See also
References
- Wilkie, H. C. (1966), "On non-Euclidean crystallographic groups", Mathematische Zeitschrift, 91: 87–102, doi:10.1007/bf01110157, MR 0185013.
- Bujalance, Emilio (1986), "Automorphism groups of compact planar Klein surfaces", Manuscripta Mathematica, 56 (1): 105–124, doi:10.1007/BF01171036, MR 846989.
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