  An integral polytope is a polytope whose vertices have integer coordinates. A
unimodular triangulation of an integral polytope in $\mathbb{R}^d$ is a
triangulation in which all simplices are integral with volume $1/d!$. A classic
result of Knudsen, Mumford, and Waterman states that for every integral
polytope $P$, there exists a positive integer $c$ such that $cP$ has a
unimodular triangulation. We strengthen this result by showing that for every
integral polytope $P$, there exists $c$ such that for every positive integer
$c' \ge c$, $c'P$ admits a unimodular triangulation. This answers a
longstanding question in the area.
