  It is proved that if $u_1,\ldots, u_n$ are vectors in ${\Bbb R}^k, k\le n, 1
\le p < \infty$ and
  $$r = ({1\over k} \sum ^n_1 |u_i|^p)^{1\over p}$$
  then the volume of the symmetric convex body whose boundary functionals are
$\pm u_1,\ldots, \pm u_n$, is bounded from below as
  $$|\{ x\in {\Bbb R}^k\colon \ |\langle x,u_i\rangle | \le 1 \ \hbox{for
every} \ i\}|^{1\over k} \ge {1\over \sqrt{\rho}r}.$$
  An application to number theory is stated.
