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In this paper, a procedure is proposed for calculating the interaction diagram of a vertical pile group subject to axial load and biaxial moments; equations are then applied to the AASHTO LRFD code. Several cases are presented, depending on the efficiency of the pile group, and it is shown that the interaction diagram can be a pentahedron, a hexahedron, an octahedron, a nonahedron, or a decahedron. It is shown how the use of convex analysis and computational geometry leads to a rationaldoi:10.1061/(asce)0733-9445(2006)132:3(460) fatcat:zd6m26z7pbcphiolettovxo5ui