Icosahedron of Resistors

Electricity and Magnetism Level 4

One of my first physics problems.

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

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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