Over the past two decades, intensive research efforts have been devoted to suppressions of Auger recombination in metal-chalcogenide and perovskite nanocrystals (PNCs) for the application of photovoltaics and light emitting devices (LEDs). Here, we have explored dodecahedron cesium lead bromide perovskite nanocrystals (DNCs), which show slower Auger recombination time compared to hexahedron nanocrystals (HNCs). We investigate many-body interactions that are manifested under high excitation flux density in both NCs using ultrafast spectroscopic pump-probe measurements. We demonstrate that the Auger recombination rate due to multiexciton recombinations are lower in DNCs than in HNCs. At low and intermediate excitation density, the majority of carriers recombine through biexcitonic recombination. However, at high excitation density (>1018 cm-3) a higher number of many-body Auger process dominates over biexcitonic recombination. Compared to HNCs, high PLQY and slower Auger recombinations in DNCs are likely to be significant for the fabrication of highly efficient perovskite-based photonics and LEDs.