Orbifold notation

In geometry, orbifold notation (or orbifold signature) is a system, invented by William Thurston and popularized by the mathematician John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature. The advantage of the notation is that it describes these groups in a way which indicates many of the groups' properties: in particular, it describes the orbifold obtained by taking the quotient of Euclidean space by the group under consideration.

Groups representable in this notation include the point groups on the sphere (${\displaystyle S^{2}}$), the frieze groups and wallpaper groups of the Euclidean plane (${\displaystyle E^{2}}$), and their analogues on the hyperbolic plane (${\displaystyle H^{2}}$).

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