A polyhedron has 33 edges and 20 faces. How many vertices does it have?
15
To find the number of vertices in a polyhedron with given edges and faces, we can use Euler's formula for polyhedra.
Euler's formula states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation:
V + F - E = 2
Given that the polyhedron has 33 edges and 20 faces, we can substitute those values into the formula:
V + 20 - 33 = 2
Simplifying the equation gives:
V - 13 = 2
Adding 13 to both sides:
V = 15
Therefore, the polyhedron has 15 vertices.