The polyhedral formula generalized to a surface of genus ,

where
is the number of polyhedron vertices, is the number of polyhedron
edges,
is the number of faces, and

is called the Euler characteristic.

## See also

Euler Characteristic,

Genus,

Polyhedral Formula
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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: ." http://www.ics.uci.edu/~eppstein/junkyard/euler/.## Referenced
on Wolfram|Alpha

Poincaré Formula
## Cite this as:

Weisstein, Eric W. "Poincaré Formula."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/PoincareFormula.html

## Subject classifications