  For any vector $r=(r_1,..., r_n)$, let $M_r$ denote the moduli space (under
rigid motions) of polygons in $\mathbb{R}^3$ with $n$-sides whose lengths are
$r_1,...,r_n$. We give an explicit characterization of the oriented
$S^1$-cobordism class of $M_r$ which depends uniquely on the length vector $r$.
