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 (
), the frieze groups and wallpaper groups of the Euclidean plane (
), and their analogues on the hyperbolic plane (
).
Definition of the notation
The following types of Euclidean transformation can occur in a group described by orbifold notation:
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