Icosahedron of Resistors
Electricity and Magnetism
Level
3
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
by
Sharky Kesa