What will be the effective resistance across 2 adjacent vertices of a regular dodecahedron (12 faces) with each edge having resistance $r$?
Here is the source for the problem, it's problem 20. on the sheet.
In the link, a typical problem is solved using symmetry (infinite square lattice, resistance between adjacent vertices) and then it is stated
It appears that such a symmetrization technique can be also applied to ﬁnite lattices.
I am looking for some ideas as to how to apply this technique to a dodecahedron. More generally, I am looking for examples where such symmetrization techniques can be used for finite lattices.