  We show that for all $n\geq 3$ and all primes $p$ there are infinitely many
simplicial toric varieties of codimension $n$ in the $2n$-dimensional affine
space whose minimum number of defining equations is equal to $n$ in
characteristic $p$, and lies between $2n-2$ and $2n$ in all other
characteristics. In particular, these are new examples of varieties which are
set-theoretic complete intersections only in one positive
characteristic.\newline
  Moreover, we show that the minimum number of binomial equations which define
these varieties in all characteristics is 4 for $n=3$ and $2n-2+{n-2\choose 2}$
whenever $n\geq 4$.
