About the Bohr-Sommerfeld polytope and the multiplicative $\mathrm{SU}(2)$-eigenvalue problem for the trinion

We study in detail the work of Jeffrey and Weitsman, especially \cite{Jeffrey:Weitsman:1992} and \cite{Jeffrey:Weitsman:1994}. In particular, we describe the manner in which the inequalities that cut out the Bohr-Sommerfeld moment polytope give rise to a solution of the $\mathrm{SU}(2)$-multiplicative eigenvalue problem for the case of three conjugacy classes.