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 fundamental domain for the action, called a Möbius triangle.
Read more about Triangle Group: Definition, Classification, Von Dyck Groups, Overlapping Tilings, History, Applications
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“There is nothing in the world that I loathe more than group activity, that communal bath where the hairy and slippery mix in a multiplication of mediocrity.”
—Vladimir Nabokov (1899–1977)