Math

Euler's Formula for Polyhedron Calculator

Use V − E + F = 2 to find the missing count for a convex polyhedron.

Calculated Output

Faces (F) 6

V − E + F 2

Formula: V − E + F = 2

Step-by-Step Breakdown

1. Values used:

2. Vertices (V) = 8

3. Edges (E) = 12

4. Faces (F, 0 = solve) = 0

6. Faces (F) = 6

7. V − E + F = 2

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The math behind it

V − E + F = 2. Leave faces at 0 and the tool solves for F = 2 − V + E.

A cube has 8 vertices and 12 edges → F = 2 − 8 + 12 = 6 faces.

Does it work for all shapes?

It holds for convex polyhedra (and any shape topologically equivalent to a sphere).