Euler's Polyhedron Formula

For every convex polyhedron, vertices minus edges plus faces equals two.

Specifications & Metrics

proved

Euler 1758; rigorously by Cauchy 1813

Core Principles & Analysis

• Descartes had the equivalent result in 1630, unpublished.
• It is the seed of topology: the count survives any deformation, only connectivity matters.
• On a doughnut surface the count comes to zero — the genus changes the arithmetic.