1. The problem is to understand the relationship between faces, vertices, and edges of a polyhedron. 2. According to Euler's formula for polyhedra, the number of vertices $V$, edges $E$, and faces $F$ satisfy the equation: $$V - E + F = 2$$ 3. This formula helps us check if a given polyhedron's counts of faces, vertices, and edges are consistent. 4. For example, if a polyhedron has 8 vertices and 12 edges, we can find the number of faces by rearranging Euler's formula: $$F = 2 - V + E = 2 - 8 + 12 = 6$$ 5. So, the polyhedron has 6 faces. 6. This relationship is fundamental in geometry and helps classify and understand polyhedra.