Triangular flux

A point charge \(q\) is located at the center of a hollow icosahedron. If the flux through one face can be expressed as \((\frac{a}{b})q/\epsilon_0\) where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

Clarification: \(\epsilon_0\) is the permittivity of free space.

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