Euler’s Polyhedron Formula

Euler’s Polyhedron Formula

Euler’s formula connects the three main counts of a polyhedron:

• V = number of vertices
• E = number of edges
• F = number of faces

For a convex polyhedron, these quantities satisfy:

V - E + F = 2

How to use it

1. Identify what is given. Look for the numbers of vertices, edges, and faces.

2. Substitute into the formula. Place the known values into V - E + F = 2.

3. Solve for the missing quantity. Rearrange the equation if needed.

   • If V is missing: V = E - F + 2
   • If E is missing: E = V + F - 2
   • If F is missing: F = 2 - V + E

4. Simplify your final answer. Carry out the arithmetic carefully and write the result in simplest form.

Good check

After finding the missing value, substitute it back into V - E + F = 2 to make sure the equation is true. If it does not equal 2, recheck your counting of vertices, edges, or faces.

Tip

Count each edge once and be careful not to confuse faces with flat parts that are not actually separate polygonal faces.