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 \(1\Omega\)?
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!