We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m_{1}≠m_{2}. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m_{2}/m_{1}=2 and list a number of geometries that are found for higher integer mass ratios.
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