The Yb-Ga-Au 1/1 quasicrystal approximant (AP) composition ranges from Yb14.0Ga20.6Au65.4 to Yb-14.8Ga46.3Au38.9, and single crystals of the 1/1 AP having the composition Yb13.8Ga26.1Au60.1 were obtained by the self-flux technique. X-ray structural analysis demonstrated that the atomic structure [space group Im (3) over bar; a = 14.6889(9) angstrom] can be described by the body-centered packing of Tsai-type rhombic triacontahedron (RTH) clusters. The positional disorder in these clusters, interpreted as the average of an orientationally disordered tetrahedron and triangle, results in positional disorder in the outer shells. The elemental distributions and positions of mixtures of Au and Ga atoms in the RTH clusters correspond to those in the isostructural Yb15Al36Au49 1/1 AP.