Euler's formula for polyhedra states that V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. Let's check if the given values satisfy this formula:
V - E + F = 15 - 20 + 10 = 5
Since the result (5) is not equal to 2, a polyhedron cannot have 10 faces, 20 edges, and 15 vertices. Euler's formula is a necessary condition for a polyhedron to exist; if it's not satisfied, the polyhedron is impossible.