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GeezerVison is showing mathworld.wolfram.com — Euler Measure -- from Wolfram MathWorld

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Euler Measure

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded convex polyhedron is always 1 (independent of dimension), while the Euler measure of a d-D relative-open bounded convex polyhedron is (-1)^d.

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References

Propp, J. "Proof of Euler-Poincare Formula." [email protected] posting, Aug. 30, 1996.

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Euler Measure

Cite this as:

Weisstein, Eric W. "Euler Measure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EulerMeasure.html

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