Orbifolds, the regular solids, and Hurwitz's \(84(g - 1)\) theorem (Q6158266)

The author presents a peculiar approach to prove some classical results; it is based on the use of orbifolds and investigation of isometries of compact surfaces with isolated fixed points. From the orbifold version of the Gauss-Bonnet theorem he deduces the classification of regular solids in the space and the classical Hurwitz result that the group of holomorphic automorphisms of a compact Riemann surface of genus \(g > 1\) has order at most \(84(g-1)\).