  For the class of non-degenerate box splines, we prove that these box splines
are piecewise polynomial. This is not a new result, it is in fact a well known
and useful property of box splines. However, our proof is constructive, and the
main result of this work is a corollary that follows from this proof, namely
one that gives an explicit construction scheme for the polynomial pieces in the
interior regions of any non-degenerate box spline.
