  We study dilute suspensions of magnetic nanoparticles in a nematic host, on
two-dimensional (2D) polygons. These systems are described by a nematic order
parameter and a spontaneous magnetization, in the absence of any external
fields. We study the stable states in terms of stable critical points of an
appropriately defined free energy, with a nemato-magnetic coupling energy. We
numerically study the interplay between the shape of the regular polygon, the
size of the polygon and the strength of the nemato-magnetic coupling for the
multistability of this prototype system. Our notable results include (i) the
co-existence of stable states with domain walls and stable interior and
boundary defects, (ii) the suppression of multistability for positive
nemato-magnetic coupling, and (iii) the enhancement of multistability for
negative nemato-magnetic coupling.
