The Euler characteristic for a convex polyhedron is given by V - E + F. What is this value?

The Euler characteristic for a convex polyhedron is given by V - E + F. What is this value?

• A. 2
• B. 0
• C. 1
• D. -2

Answer: (A)

In convex polyhedra, the surface behaves like a sphere topologically, so Euler’s characteristic is fixed at 2. The quantity V − E + F, where V counts vertices, E counts edges, and F counts faces, must equal that characteristic. This is a universal property: for any convex polyhedron, V − E + F = 2. For a concrete check, a cube has 8 vertices, 12 edges, and 6 faces, giving 8 − 12 + 6 = 2. So the value is 2.

In convex polyhedra, the surface behaves like a sphere topologically, so Euler’s characteristic is fixed at 2. The quantity V − E + F, where V counts vertices, E counts edges, and F counts faces, must equal that characteristic. This is a universal property: for any convex polyhedron, V − E + F = 2. For a concrete check, a cube has 8 vertices, 12 edges, and 6 faces, giving 8 − 12 + 6 = 2. So the value is 2.