Euler characteristic

The Euler characteristic is one of the important quantities, known as a topological invariant, that describes the shape or structure of topological space. Leonhard Euler originally formulated the characteristic for polyhedra and used it to prove various theorems about them, including the classification of the Platonic solids. For the special case of polyhedra, the Euler characteristic equals 2 (see Euler's formula for polyhedra).


In algebraic topology, the Euler characteristic arises from homology and connects to many other invariants.