1. **Stating the problem:** Find the number of faces (F), edges (E), and vertices (V) for each solid: tetrahedron and cube. Write an equation relating F, E, and V. Check if the equation works for other solids. 2. **Formula used:** Euler's formula for polyhedra states: $$F - E + V = 2$$ This formula applies to convex polyhedra, including Platonic solids. 3. **Given data:** - Tetrahedron: $F=4$, $E=6$, $V=4$ - Cube: $F=6$, $E=12$, $V=8$ 4. **Check Euler's formula for tetrahedron:** $$4 - 6 + 4 = 2$$ $$2 = 2$$ The equation holds. 5. **Check Euler's formula for cube:** $$6 - 12 + 8 = 2$$ $$2 = 2$$ The equation holds. 6. **Conclusion:** Euler's formula $F - E + V = 2$ correctly relates the number of faces, edges, and vertices for these Platonic solids. It also works for other convex polyhedra. Final answer: Euler's formula is $$F - E + V = 2$$ and it holds for the tetrahedron and cube given.