The manganese orthophosphate, Mn-3(PO4)(2), is characterized by the rich variety of polymorphous modifications, alpha-, beta'-, and gamma-phases, crystallized in monoclinic P2(1)/c (P2(1)/n) space group type with unit cell volume ratios of 2:6:1. The crystal structures of these phases are constituted by three-dimensional framework of corner- and edge-sharing [MnO5] and [MnO6] polyhedra strengthened by [PO4] tetrahedra. All compounds experience long-range antiferromagnetic order at Neel temperature T-N = 21.9 K (alpha-phase), 12.3 K (beta'-phase), and 13.3 K (gamma-phase). Additionally, second magnetic phase transition takes place at T* = 10.3 K in beta'-phase. The magnetization curves of alpha- and, beta'-modifications evidence spin-floplike features at B = 1.9 and 3.7 T, while the gamma-Mn-3(PO4)(2) stands out for an extended one-third magnetization plateau stabilized in the range of magnetic field B = 7.5-23.5 T. The first-principles calculations define the main paths of superexchange interaction between Mn spins in these polymorphs. The spin model for alpha-phase is found to be characterized by collection of uniform and alternating chains, which are coupled in all three directions. The strongest magnetic exchange interaction in gamma-phase emphasizes the trimer units, which make chains that are in turn weakly coupled to each other. The spin model of beta'-phase turns out to be more complex compared to alpha- or gamma-phase. It shows complex chain structures involving exchange interactions between Mn-2 (Mn2', Mn2 '') and Mn3 (Mn3', Mn3 ''). These chains interact through exchanges involving Mn1 (Mn1', Mn1 '') spins.