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, that gives (many) polyhedral models for any Lie type.

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 (Inventiones mathematicae 143 (2001) pp 77–128, https://doi.org/10.1007/s002220000102), that gives (many) polyhedral models for any Lie type.