MathLiveEuler characteristic of a polyhedron
The Euler characteristic gives an integer that counts vertices minus edges plus faces of a polyhedron, and for a convex polyhedron it equals 2. More generally it is an alternating sum of Betti numbers or cell counts, a topological invariant that helps distinguish and classify surfaces and other spaces.
\chi=V-E+FWhat the symbols mean
| Euler characteristic (dimensionless integer) | |
| number of vertices | |
| number of edges | |
| number of faces |
About this formula
- FieldMathematics
- TopicTopology
- LevelUniversity
- Also calledEuler polyhedron formula, V minus E plus F, vertices edges faces formula, Euler characteristic, Euler-Poincaré characteristic, Euler's polyhedron theorem
- SourceWikidata Q852973
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