In Dekker (2019), while arguing for the use of agent-based computer simulation as a tool for understanding the function of anthropological phenomena, we explored the system of 8 "skin groups" or "subsections" used across central northern Australia (Figure 1). We noted in passing the well-known fact that this system has the structure of the dihedral group D 4 . In this paper, we address the question: why D 4 ? We report further analyses and NetLogo-based simulations comparing this system against alternative structures derived from group theory, and show that this system based on D 4 was indeed better than the alternatives: genetically, in story transmission, and with regard to formal properties. Table 1 summarises our findings.