  This paper studies the configuration spaces of linkages whose underlying
graph is a single cycle. Assume that the edge lengths are such that there are
no configurations in which all the edges lie along a line. The main results are
that, modulo translations and rotations, each component of the space of convex
configurations is homeomorphic to a closed Euclidean ball and each component of
the space of embedded configurations is homeomorphic to a Euclidean space. This
represents an elaboration on the topological information that follows from the
convexification theorem of Connelly, Demaine, and Rote.
