We report the synthesis and crystal structure of a new phase in the Mg-Cu-Al system: Mg11Cu6Al12. This compound crystallizes in the K17In41 structure type. When written asMg17–xCuxAl12, x = 6, the composition of this phase foretells a connection to Mg17Al12 (α-Mn type). The structures of both can be constructed from 29-atom fragments of the MgCu2 structure type. They differ in the orientations of these fragments: the Mg11Cu6Al12 structure is obtained when half of the MgCu2-type clusters of Mg17Al12 are rotated by 90°. Electronic structure calculations using density functional theory (DFT) and the extended Hückel (eH) method point to driving forces for this structural transformation. Density of states (DOS) curves calculated for Mg11Cu6Al12 in the two structure types indicate that both are stabilized by DOS minima close to the Fermi energy, with the pseudogap being deeper for the observed structure. An eH relative Mulliken population analysis reveals that cluster rotation also changes the electronic character of the outermost sites of the MgCu2-type fragments: six atoms per formula unit go from being ambiguous to anionic, and thus suitable to occupation by relatively electronegative elements. These are the positions occupied by Cu in Mg11Cu6Al12. The creation of these six anionic sites adapted to occupation by Cu provides an impetus for cluster rotation. The removal of ambiguity of the outermost sites of the MgCu2-type fragments creates extended networks of anionic and cationic sites in Mg11Cu6Al12. The cationic sites trace out the clathrate II framework noted by Corbett and co-workers in the K17In41 type, while the anionic sites ensheathe this framework to complete Friauf polyhedra around the framework atoms.