  The real solutions to a system of sparse polynomial equations may be realized
as a fiber of a projection map from a toric variety. When the toric variety is
orientable, the degree of this map is a lower bound for the number of real
solutions to the system of equations. We strengthen previous work by
characterizing when the toric variety is orientable. This is based on work of
Nakayama and Nishimura, who characterized the orientability of smooth real
toric varieties.
