# Resistors On A Dodecahedron

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

A dodecahedron has 20 vertices and 30 edges with 3 edges meeting at each vertex.

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