Synthetic explorations in the quaternary Li-Mg-Cu-Ga system yield the novel intermetallic Li-14.7(8)-Mg36.8(13)Cu21.5(5)Ga66 [P (6) over bar m2, Z = 1, a = 14.0803(4) angstrom, c = 13.6252 (8) angstrom] from within a limited composition range. This contains a unique three-dimensional anionic framework consisting of distinct interbonded Ga-12 icosahedra, dimerized Li@(Cu,Mg)(10)Ga-6 icosioctahedra, and 15-vertex Li@(Cu,Mg)(9)Ga-6 and Li@Cu3Ga12 polyhedra. These polyhedral clusters are hosted by M-20 (5(12)), M-24 (5(12)6(2)), and M-26 (5(12)6(3)) (M = Li/Mg) cages, respectively. The geometries and arrangements of these cages follow those in known type IV clathrate hydrates.