  For ell a generic n-tuple of positive numbers, N(ell) denotes the space of
isometry classes of oriented n-gons in R^3 with side lengths specified by ell.
We determine the algebra K(N(ell)) and use this to obtain nonimmersions of the
2(n-3)-manifold N(ell) in Euclidean space for several families of ell. We also
use obstruction theory to tell exactly when N(ell) immerses in R^{4n-14} for
two families of ell.
