# Counterexamples to Euler's Formula for Nonconvex Polyhedra

Counterexamples to Euler's Formula for Nonconvex Polyhedra

The Demonstration shows three counterexamples to Euler's formula, , where , , and are the number of vertices, edges, and faces, respectively. The formula holds for all polyhedra, so the exercise here is to see how these figures fail the proper definition of being a polyhedron.

V-E+F=2

V

E

F