For each given polytope, let the vertices be connected by 1-ohm resistors along the polytope's edges.
1. What is the resistance between two opposite vertices of a cube?
2. What is the resistance between two opposite vertices of an octahedron?
3. What is the resistance between any two distinct vertices of a tetrahedron?
4. Generalize the answers of the previous answers to the corresponding n-dimensional polytopes.