High Quality Content by WIKIPEDIA articles! 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.