We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m1≠m2. 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 m2/m1=2 and list a number of geometries that are found for higher integer mass ratios.