For a compact topological surface with cone-point orders , the orbifold Euler characteristic is . An orbifold covering multiplies this quantity by its degree.

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Orbifold by Wikipedia Bot 1
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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.
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