 Orbifold

An orbifold is locally modeled on a quotient $U/G$ of an open subset of Euclidean space by a finite group action, with compatible quotient charts. The chart retains the local group action, not merely the underlying quotient topological space. For example, the plane modulo a rotation of order $m$ has a cone point with total angle $2\pi /m$. Its underlying space is homeomorphic to a plane, but its orbifold structure records the order-$m$ stabilizer. If every stabilizer is trivial, the local models reduce to those of a manifold.

An orbifold is a generalization of a manifold that allows for certain types of singularities. More formally, an orbifold can be defined as a space that looks locally like a manifold but may have points where the structure of the space is modified by a finite group acting on it.