Synthetic explorations in the quaternary Li−Mg−Cu−Ga system yield the novel intermetallic Li14.7(8)Mg36.8(13)Cu21.5(5)Ga66 [P6̅m2, Z = 1, a = 14.0803(4) Å, c = 13.6252 (8) Å] from within a limited composition range. This contains a unique three-dimensional anionic framework consisting of distinct interbonded Ga12 icosahedra, dimerized Li@(Cu,Mg)10Ga6 icosioctahedra, and 15-vertex Li@(Cu,Mg)9Ga6 and Li@Cu3Ga12 polyhedra. These polyhedral clusters are hosted by M20 (512), M24 (51262), and M26 (51263) (M = Li/Mg) cages, respectively. The geometries and arrangements of these cages follow those in known type IV clathrate hydrates.