 Orbifold Euler characteristic (source code)

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= Orbifold Euler characteristic
{title2=$\chi_{\mathrm{orb}}$}

For a compact <topological surface> with cone-point orders $\alpha_1,\ldots,\alpha_k$, the orbifold Euler characteristic is $\chi_{\mathrm{orb}}=\chi(\text{underlying surface})-\sum_i(1-1/\alpha_i)$. An orbifold covering multiplies this quantity by its degree.

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