Euler's Polyhedral Formula

name

cube

tetrahedron

octahedron

dodecahedron

icosahedron

Let the number of vertices, edges, and faces of a polyhedron be

V

,

E

, and

F

. The Euler characteristic,

V-F+E

, is always 2 for convex polyhedra. This Demonstration shows Euler's polyhedral formula

V+F-E=2

for the Platonic solids.