We obtain two isospin amplitude decompositions of the B→Kππ decays. We use the method of addition of three isospin vectors, and prove the equivalency of the two isospin amplitude decompositions obtained. We only have considered contributions of the Hamiltonian to the transitions with change of isospin ΔI=0 and ΔI=1. The symmetry of isospin allows to relate the charged B+→K+π+π−, B+→K+π0π0, and B+→K0π0π+ channels with the neutral B0→K0π+π−, B0→K0π0π0, and B0→K+π0π− channels. Additionally, we obtain equivalent triangular relations in the charged and neutral channels.