  A two species interacting system motivated by the density functional theory
for triblock copolymers contains long range interaction that affects the two
species differently. In a two species periodic assembly of discs, the two
species appear alternately on a lattice. A minimal two species periodic
assembly is one with the least energy per lattice cell area. There is a
parameter $b$ in $[0,1]$ and the type of the lattice associated with a minimal
assembly varies depending on $b$. There are several thresholds defined by a
number $B=0.1867...$ If $b \in [0, B)$, a minimal assembly is associated with a
rectangular lattice whose ratio of the longer side and the shorter side is in
$[\sqrt{3}, 1)$; if $b \in [B, 1-B]$, a minimal assembly is associated with a
square lattice; if $b \in (1-B, 1]$, a minimal assembly is associated with a
rhombic lattice with an acute angle in $[\frac{\pi}{3}, \frac{\pi}{2})$. Only
when $b=1$, this rhombic lattice is a hexagonal lattice. None of the other
values of $b$ yields a hexagonal lattice, a sharp contrast to the situation for
one species interacting systems, where hexagonal lattices are ubiquitously
observed.
