An understanding of the structural stability and formation mechanism of ligated gold nanoclusters with triply coordinated mu(3)-sulfido (mu(3)-S) motifs is important not only for gold chemistry but also for the design of more effective catalysts or drug carriers for various applications. In this article, a new elementary block Au-3(mu(3)-S) with zero valence electrons [referred to as Au-3(mu(3)-S)(0e)] has been identified, which describes all crystallized ligated gold clusters with mu(3)-S motifs, in conjunction with the previously reported Au-3(2e) and Au-4(2e) elementary blocks, in a grand unified model (GUM). This Au-3(mu(3)-S)(0e) elementary block has a tripod structure with the S atom bonding to three Au atoms in a mu(3) bridging mode, and can be considered as a mu(3)-S atom balancing out the 2e valence electrons of the Au-3(2e) block. Using Au-3(mu(3)-S) as a building block, a special group of quasi-fullerene hollow-cage [Au(3)n(mu(3)-S)(2n)](n-) gold(I) mu(3)-S clusters are designed, which exhibit high stabilities. In addition, a series of theoretical structures are predicted to be increasingly stable after introducing mu(3)-S atoms, based on the crystallized clusters. Overall, the introduction of a Au-3(mu(3)-S)(0e) elementary block can help with the understanding of diverse structures of ligated gold clusters with mu(3)-S motifs, thereby assisting the rational design of new forms of gold nanoclusters.