Euler’s Polyhedron Formula: V + F − E = 2Discovered by Leonhard Euler in 1752, this simple...

Euler’s Polyhedron Formula: V + F − E = 2

Discovered by Leonhard Euler in 1752, this simple but powerful formula states that in any regular polyhedron, the number of vertices V and faces F is always two more than the number of edges E. (a) Verify the formula for a simple cube. (b) Verify the formula for the octahedron shown in the figure. (c) If a dodecahedron has 12 faces and 30 edges, how many vertices does it have?