A series of ternary and quaternary R-phase compounds in the Li-Mg-Zn-Al system are synthesized from pure elements in sealed Ta tubes with starting compositions based on the suggestions from electronic structure calculations using relative Mulliken populations to quantify the site preferences for the various elements. Single-crystal structural analyses reveal new R-phase compounds with various Li/Mg and Zn/Al ratios. The space group of all compounds is Im3̄ (No. 204). Five quaternary phases [Li1.00(1)Mg0.63(2)Zn1.23(1) Al2.14(1) (1), a = 14.073(3) Å; Li1.00(1)Mg0.63(1)Zn1.42(1) Al1.96(1) (2), a = 14.088(3) Å; Li1.01(1)Mg0.62(1)Zn1.31(1) Al2.06(1) (3), a = 14.096(5) Å;Li1.03(1)- Mg0.60(1)Zn1.78(3)Al1.59(3) (4), a = 13.993(5) Å; Li0.78(2)Mg0.85(2)Zn2.47(1) Al0.94(1) (5), a = 13.933(2) Å] and four ternary compounds [Li1.63Zn0.81(1)Al2.56(1) (6), a = 14.135(3) Å; Li1.63Zn1.42(1)Al1.95(1) (7), a = 13.966(5) Å Li1.63-Zn1.59(1) Al1.78(1) (8), a = 13.947(2) Å; and Li1.63Zn1.77(1) Al1.60(1) (9), a = 13.933(4) Å] are identified. The crystal structure exhibits an Al/Zn (M sites) network constructed from M12 icosahedra and M60 buckyball-type clusters. Li/Mg atoms (A sites) fill cavities within the Al/Zn network to give pentagonal dodecahedra (A20). The site-potential studies (relative Mulliken populations) indicate two groups of atomic sites (positively and negatively polarized), which are consistent with the single-crystal studies. Further differentiation of site potentials among the various electropositive sites leads to segregation of Li and Mg, which is also verified experimentally. The analysis of relative Mulliken populations in an intermetallic framework provides a useful method for elucidating elemental site preferences when diffraction techniques cannot unequivocally solve the site preference problem.