## ::Euler characteristic

### ::concepts

Euler::image Number::space ''F''::''v'' ''E''::graph Minus::formula Faces::finite

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the **Euler characteristic** (or **Euler number**, or **Euler–PoincarĂ© characteristic**) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent. It is commonly denoted by <math> \chi </math> (Greek lower-case letter chi).

The Euler characteristic was originally defined for polyhedra and used to prove various theorems about them, including the classification of the Platonic solids. Leonhard Euler, for whom the concept is named, was responsible for much of this early work. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra.

**Euler characteristic sections**

Intro Polyhedra Topological definition Properties Examples Relations to other invariants Generalizations See also References Further reading External links

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