You have each of the five Platonic solids, with edges made out of $1\Omega$ resistors. For which solid can you pick two vertices that have an effective resistance between them that is greater than $1\Omega$?

**Definitions**:

*Tetrahedron*is a polyhedron with 4 sides.*Octahedron*is a polyhedron with 8 flat faces.*Dodecahedron*is a polyhedron with 12 flat faces.*Icosahedron*is a polyhedron with 20 flat faces.*Oblate spheroid*is a quadric surface obtained by rotating an ellipse about its minor axis.

**Clarification**: "All of these" and "None of these" refer only to the geometrical answers not to each other!