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${\pi }_j^i:B_i\to B_{ij}=B_{ji}$, i,j ∈ 1,2,3, i ≠ j, of C*-epimorphisms assuming that it satisfies the cocycle condition. Then we show how to compute the K-groups of the multi-pullback C*-algebra of such a family, and exemplify it in the case of the triple-Toeplitz deformation of ℂP².