A defining characteristic of the human vocal tract is a complex dynamic between structure and variability. Across a population we observe considerable variability in vocal tract dimensions, but variation in one dimension is rarely independent of other dimensions. Are some of these relationships more variable than others, or do there exist invariants in the morphology of the vocal tract? In this study, we report a data-driven investigation into the relationship between vocal tract dimensions based on multi-speaker real-time magnetic resonance imaging data. We discover different sub-populations in the data, which correspond to groups of speakers that share a common relationship between vocal tract parameters. This suggests a range of complex patterns of co-variation in the morphology of the human vocal tract. We conclude by speculating on the possible implications of these results for understanding individual differences in speech production.