Euler characteristic
Geometry and topology
A number attached to a space, computed for a polyhedron as vertices minus edges plus faces, and unchanged by continuous deformation.
What is usually left out
Every convex polyhedron gives V − E + F = 2, because each is topologically a sphere — the invariant belongs to the shape, not the subdivision. A torus gives 0 instead, so the quantity distinguishes surfaces that no amount of counting faces alone would.