  Macdonald studied a discrete volume measure for a rational polytope $P$,
called solid angle sum, that gives a natural discrete volume for $P$. We give a
local formula for the codimension two quasi-coefficient of the solid angle sum
of $P$. We also show how to recover the classical Ehrhart quasi-polynomial from
the solid angle sum and in particular we find a similar local formula for the
codimension one and codimension two quasi-coefficients. These local formulas
are naturally valid for all positive real dilates of $P$.
  An interesting open question is to determine necessary and sufficient
conditions on a polytope $P$ for which the discrete volume of $P$ given by the
solid angle sum equals its continuous volume: $A_P(t) = \mathrm{vol}(P) t^d$.
We prove that a sufficient condition is that $P$ tiles $\mathbb R^d$ by
translations, together with the Hyperoctahedral group.
