Topology studies what remains after geometry has been allowed to move.

Euler’s characteristic is a number that describes the fundamental structure of a geometric or topological object. For a polyhedron, it is commonly calculated as χ = V − E + F, where V is the number of vertices, E the number of edges, and F the number of faces. For a convex polyhedron, the result is always 2, regardless of its particular shape. More generally, Euler’s characteristic remains unchanged under continuous deformations, making it an important topological invariant. It helps distinguish surfaces and reveals structural relationships that are not obvious from geometry alone. It is used in topology, geometry, graph theory, and differential geometry.