Plastic flow states corresponding to an edge of the Coulomb-Tresca prism in the Haigh-Westergaard three-dimensional space of principal stresses are considered. Constitutive equations are formulated by the generalized associated plastic flow rule due to Koiter. These equations impose the minimal kinematical constraints on plastic strains increments and as it is elucidated are equivalent to three-dimensional equations of the mathematical plasticity proposed by Ishlinskii in 1946. It is then shown that obtained constitutive equations can be formulated as a tensor permutability equation for the stress tensor and the plastic strains tensor increment. A new explicit form of the plastic flow rule for stress states corresponding to an edge of the Coulomb-Tresca prism is obtained and discussed.