Twelve equal wires , each of resistance r ohm are connected so as to form a skeleton cube. Find the equivalent resistance between the diagonally opposite points 1 and 7.

Explanation

Connect a source between point 1 and 7
The network is symmetrical about the diagonal 1-7 . Therefore current in resistors are distributed symmetrically about the diagonal . The current distribution is shown in fig(b) .
Choose a close loop 1-2-3-7-9-10-1, we have `-r1/3 ri/6 ri/3 + V=0 ` (or) `V/i = 5/6 r`
(or)` R_(17) = V/i = 5/6 r`