Icosahedron of Resistors

One of my first physics problems.

Each edge of an icosahedron is a 1­ Ω\Omega resistor. If the effective resistance between two adjacent vertices can be represented as abΩ\frac {a}{b} \Omega where aa and bb are co-prime positive integers, find a+ba + b.

An icosahedron consists of 20 equilateral triangles. It has 12 vertices and 30 edges, with 5 edges meeting at each vertex.

Image credit: Wikipedia DTR

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