  There is a standard method to calculate the cohomology of torus-invariant
sheaves $L$ on a toric variety via the simplicial cohomology of associated
subsets $V(L)$ of the space $N_{\mathbb R}$ of 1-parameter subgroups of the
torus. For a line bundle $L$ represented by a formal difference
$\Delta^+-\Delta^-$ of polyhedra in the character space $M_{\mathbb R}$,
[ABKW18] contains a simpler formula for the cohomology of $L$, replacing $V(L)$
by the set-theoretic difference $\Delta^- \setminus \Delta^+$. Here, we provide
a short and direct proof of this formula.
