  When a two-component Bose-Einstein condensate is placed into rotation, a
lattice of vortices and cores appear. The geometry of this lattice (triangular
or square) varies according to the rotational value and the intercomponent
coupling strengths. In this paper, assuming a Thomas-Fermi regime, we derive a
point energy which allows us to determine for which values of the parameters,
the lattice goes from triangular to square. It turns out that the separating
curve in the phase diagram agrees fully with the complete numerical simulations
of the Gross-Pitaevskii equations. We also derive a formula for the critical
velocity of appearance of the first vortex and prove that the first vortex
always appears first in the component with largest support in the case of two
disks, and give a criterion in the case of disk and annulus.
