1. The problem asks us to apply Euler's Formula to determine if an octahedron is a polyhedron. 2. Euler's Formula for polyhedra states: $$V - E + F = 2$$ where $V$ is the number of vertices, $E$ is the number of edges, and $F$ is the number of faces. 3. For a regular octahedron: - Number of vertices, $V = 6$ - Number of edges, $E = 12$ - Number of faces, $F = 8$ 4. Substitute these values into Euler's Formula: $$6 - 12 + 8 = 2$$ 5. Simplify the left side: $$6 - 12 + 8 = (6 - 12) + 8 = -6 + 8 = 2$$ 6. Since the equation holds true, the octahedron satisfies Euler's Formula. 7. Therefore, the octahedron is indeed a polyhedron.