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New ternary dodeca­lithium dodeca­copper tetra­deca­aluminium, Li12Cu12.60Al14.37 (trigonal, R\overline{3}m, hR39), crystallizes as a new structure type and belongs to the structural family that derives from binary Laves phases. The Li atoms are enclosed in 15- and 16-vertex and the Al3 atom in 14-vertex pseudo-Frank–Kasper polyhedra. The polyhedra around the statistical mixtures of (Cu,Al)1 and (Al,Cu)2 are distorted icosa­hedra. The electronic structure was calculated by the TB–LMTO–ASA (tight-binding linear muffin-tin orbital atomic spheres approximation) method. The electron localization function, which indicates bond formation, is mostly located at the Al atoms. Thus, Al—Al bonding is much stronger than Li—Al or Cu—Al bonding. This indicates that, besides metallic bonding which is dominant in this compound, weak covalent Al—Al inter­actions also exist.