  Among integral polytopes (vertices with integral coordinates), lattice-free
polytopes - intersecting the lattice ONLY at their vertices- are of particular
interestin combinatorics and geometry of numbers.
  A natural question is to measure their "width" (with respect to the integral
lattice).There were no known examples of lattice-free polytopes with width
bigger than 2 .We prove the following Theorem : Given any positive number
$\alpha$ strictly inferior to $1/e$, for d large enough there exists a
lattice-free simplex of dimension d and width superior to $\alpha d$.
