  In this article, we construct matrices associated to Pachner
$\frac{n-1}{2}$-$\frac{n-1}{2}$ moves for odd $n$ and matrices associated to
Pachner $(\frac{n}{2}-1)$-$\frac{n}{2}$ moves for even $n$. The entries of
these matrices are rational functions of formal variables in a field. We prove
that these matrices satisfy the $n$-gon equation for any $n$.
