Triangular Au3 and tetrahedral Au4 are key structural units in the face-centered cubic gold core of thiolate-protected gold nanoclusters. Understanding their stacking arrangements is essential for elucidating the growth mechanisms of these gold cores. In this study, we design two new isomers of Au29(SR)19 nanoclusters via deliberately adjusting the stacking pattern of Au3 and Au4 based on the grand unified model and ring model to show preferable packing arrangements. Among the experimental isomer and the two newly constructed isomers of Au29(SR)19, the Au3 and Au4 units display three distinct stacking arrangements: completely independent Au3; Au3 sharing a vertex with one Au4; and Au3 sharing vertices with two Au4. Density functional theory calculations reveal that the isomer with a completely independent Au3 unit owns the lower relative energy, which suggests that forming independent Au3 in thiolate-protected gold nanoclusters is relatively straightforward, while achieving alternative stacking configurations with Au3 and Au4 is more challenging, aligning with experimental observations. This study provides a theoretical foundation for understanding the stacking arrangements between triangular Au3 and tetrahedral Au4 units, offering valuable insights for designing ligand-protected gold nanoclusters featuring triangular Au3 units.