Brilliant's Brilliant LOGO

The Brilliant logo is similar in appearance to a Disdyakis triacontahedron, a Catalan solid. Suppose we had a circuit consisting of the edges and vertices of one of these solids, and the resistance along any edge is \(1\, \Omega.\)

The North and South pole vertices of this solid each have 10 connected edges. Determine the equivalent resistance between the poles of the solid in \(\Omega.\)

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