  We investigate a mixture of two repulsively interacting superfluids with
different constituent particle masses: $m_1\ne m_2$. 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.
