High Quality Content by WIKIPEDIA articles! In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere or the hyperbolic plane by congruent triangles. A triangle group ?(l,m,n) is a group of motions of the Euclidean plane, the two-dimensional sphere, or the hyperbolic plane.

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