When Wires Turn Useless

I guess I will never fall short of useless wire. This time I had a wire with a total resistance of \(15 \Omega\) and then I cut it into 30 equal pieces to form a regular Icosahedron as shown below. Then what is the equivalent resistance between any two opposite nodes in \(\Omega\)?

If the equivalent resistance between any two opposite nodes is \(R\), then enter the value of \(100R\).


Image credit:Wikipedia
This question is part of the set Platonic Electricity.
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