The magnetic structures of the Cu2O3 spin lattices present in Cu4O3 and Ag2Cu2O3 were analyzed by studying their spin exchange interactions on the basis of spin dimer analysis. Calculations of spin exchange parameters were calibrated by studying LiCuVO4 whose intrachain and interchain antiferromagnetic spin exchange parameters are known experimentally. The magnetic phase transition of Cu4O3 at 42.3 K doubles the unit cell along each crystallographic direction. The spin arrangements of the Cu2O3 lattice consistent with this experimental observation are different from conventional antiferromagnetic ordering. Our analysis indicates that spin fluctuation should occur in Cu4O3, low-dimensional magnetism should be more important than magnetic frustration in Cu4O3, and Ag2Cu2O3 and Cu4O3 should have similar structural and magnetic properties.