• IntroductionEuler characteristic
  • PolyhedraPlane graphsProof of Euler's formula
  • Topological definitionBetti number alternative
  • PropertiesHomotopy invarianceInclusion–exclusion principleConnected sumProduct propertyCovering spacesFibration property
  • ExamplesSurfacesSoccer ballArbitrary dimensions
  • Relations to other invariants
  • Generalizations
  • See also
  • ReferencesNotesBibliography
  • Further reading
  • External links