Parreira J. R. Some Symmetry Remarks on the Ground State Configurations of the Two Dimensional Bosonic Falicov-Kimball Model (18K, LaTeX) ABSTRACT. We show that the ground state configuration of the nuclei in a system composed by itinerant bosons described by the Falicov-Kimball Hamiltonian in two dimensions is composed by symmetric intervals centered on $45^{\circ}$-lines on the cartesian plane. This adds up to the previous result about this problem which asserted symmetry of intervals with centered on the coordinate axii. The combination of these facts strongly suggest the convexity of nuclear distributions.