Poincaré Formula
The polyhedral formula generalized to a surface of genus g,
| V-E+F=chi(g) |
where V is the number of polyhedron vertices, E is the number of polyhedron edges, F is the number of faces, and
| chi(g)=2-2g |
is called the Euler characteristic.
See also
Euler Characteristic, Genus, Polyhedral FormulaExplore with Wolfram|Alpha
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References
Coxeter, H. S. M. "Poincaré's Proof of Euler's Formula." Ch. 9 in Regular Polytopes, 3rd ed. New York: Dover, pp. 165-172, 1973.Eppstein, D. "Fourteen Proofs of Euler's Formula: V-E+F=2." http://www.ics.uci.edu/~eppstein/junkyard/euler/.Referenced on Wolfram|Alpha
Poincaré FormulaCite this as:
Weisstein, Eric W. "Poincaré Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PoincareFormula.html