# Maximizing the conduction

Ashish has a set of 12 resistances, each are equal in length but there resistance are in geometric progression. The smallest resistance is $$1\space \Omega$$ and the common ratio is $$2$$. Now, Ashish being curious boy arranged them such that the twelve resistance formed a regular octahedron as shown below. He also wanted the circuit to conduct maximum current. So he adjusted the resistances in a unique configuration such that equivalent resistance between a particular pair of opposite nodes is the minimum.

Now, what is the resistance $$in \space \Omega$$ that Ashish achieved for maximum conduction.