Euler's formula

A simple and universal relation links the number of vertices, edges and faces of every convex polyhedron.

Theorem — Euler's formula

For every convex polyhedron: $V - S + F = 2,$ where $V$ is the number of vertices, $S$ that of the edges and $F$ that of the faces.

Check on the first Platonic solids: tetrahedron $4-6+4=2$ ✓, cube $8-12+6=2$ ✓, octahedron $6-12+8=2$ ✓.

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Topics: Synthetic geometry in space
Concepts: Euler’s formula · Polyhedron
Skills: Synthetic geometry
People: Leonhard Euler