# Platonic Resistance

**Electricity and Magnetism**Level 4

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!