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. See also Non-Euclidean geometry Isometry group Fuchsian group Uniform tilings in hyperbolic plane References . . . Non-Euclidean geometry Hyperbolic geometry Symmetry Discrete groups