There are conjectural ones in the Berenstein-Zelevinsky paper referenced in that one. They have another paper with a general theorem, _[Tensor product multiplicities, canonical bases and totally positive varieties][1]_ (Inventiones mathematicae **143** (2001) pp 77–128, https://doi.org/10.1007/s002220000102), that gives (many) polyhedral models for any Lie type.


  [1]: https://arxiv.org/abs/math/9912012