The quaternary magnetic oxide Bi4Cu3V2O14 consists Of Cu4O8 triple chains made up of corner-sharing CuO4 square planes. To determine its spin-lattice, the spin exchange interactions of Bi4Cu3V2O14 were evaluated by performing a spin dimer analysis based on tight-binding calculations and a mapping analysis based on first principles density functional theory calculations. Both calculations show that the spin-lattice of Bi4Cu3V2O14 is not an antiferromagnetically coupled diamond chain, which results from an idealized view of the structure of the Cu4O8 triple chain and a neglect of super-superexchange interactions. The correct spin-lattice is an antiferromagnetic chain made up of antiferromagnetic linear trimers coupled through their midpoints via super-superexchange interaction, which predicts that Bi4Cu3V2O14 has an antiferromagnetic spin ground state and has no spin frustration, both in agreement with experiment.