We evaluated the intrachain and interchain spin exchanges of Cu-3(P2O6OH) consisting of (Cu2-Cu2-Cu1)(infinity) chains by density functional calculations to find that the magnetic properties of Cu-3(P2O6OH)(2) are not governed by the J(1)-J(2)-J(2) trimer chain along the c-direction, but by a two-dimensional (2D) antiferromagnetic lattice in which J(1)-J(3)-J(3) trimer chains along the (a-d2)-direction are interconnected by J(6) monomer chains along the a-direction Despite its 2D character, Cu-3(P2O6OH)(2) shows a 1/3 magnetization plateau because it is a spin-1/2 trimer system with one dominant antiferromagnetic dimer exchange