  We investigate the deposition of binary mixtures of oriented superdisks on a
plane. Superdisks are chosen as objects bounded by $|x|^{2p}+|y|^{2p}=1$, where
parameter $p$ controls their size and shape. For single-type superdisks, the
maximum packing and jamming densities are known to be nonanalytic at $p=0.5$.
For binary mixtures, we discover that nonanalyticities form a locus of points
separating "phase diagram" of shape combinations into regions with different
excluded-area constructions. An analytical expression for this phase boundary
and exact constructions of the excluded-areas are presented.
