The Posner molecule, Ca9(PO4)6, has long been recognized to have biochemical relevance in various physiological processes. It has found recent attention for its possible role as a biological quantum information processor, whereby the molecule purportedly maintains long-lived nuclear spin coherences among its 31P nuclei (presumed to be symmetrically arranged), allowing it to function as a room temperature qubit. The structure of the molecule has been of much dispute in the literature, although the S6 point group symmetry has often been assumed and exploited in calculations. Using a variety of simulation techniques (including ab initio molecular dynamics and structural relaxation), rigorous data analysis tools, and by exploring thousands of individual configurations, we establish that the molecule predominantly assumes low-symmetry structures (Cs and Ci) at room temperature, as opposed to the higher-symmetry configurations explored previously. Our findings have important implications for the viability of this molecule as a qubit.