Cubic NaZn13-type (Fm-3c, Z = 8) BaAuxZn13-x compounds in the regions 1 <= x <= 5.4 (a = 12.418(1)-12.590(1) angstrom) and 6.4 <= x <= 8 (a = 12.630(1)- 12.660(1) angstrom) plus an ordered tetragonal variant near x = 6 (P4/nbm; a = 8.8945(4) angstrom, c = 12.646(1) angstrom; z = 4) have been synthesized and characterized by means of X-ray diffraction. Although the cubic structure contains Zn-centered, mixed (Zn, Au) icosahedra connected in alternate orientations via mixed tetrahedral stars (TS), the icosahedron vertices are ordered in the tetragonal structure. Both the inner and the outer tetrahedra in the TS in the cubic phase consist of mixed Au and Zn atoms, whereas the tetragonal phase features three different coloring schemes: inner Zn and outer Au tetrahedra, vice versa, or mixed Au and Zn sites on both inner and outer tetrahedra. Barium atoms center 24-atom snub cuboctahedra. Ordering of Au and Zn in the tetragonal phase achieves the largest number of heteroatomic Au-Zn contacts and yields relatively larger Hamilton populations (-ICOHPs) compared with homoatomic counterparts according to LMTO-based electronic structure calculations and analysis. Larger overlap populations are also observed for inter- versus intraicosahedral interactions. The densities-of-states data suggest the phase is metallic with highly dispersed Au d bands and nearly free-electron-like s and p bands for both Au and Zn.