Embedding cones over trees into their symmetric products

Given a metric continuum X and a positive integer n, let Fn(X) be the hyperspace of nonempty sets of X with at most n points and let Cone(X) be the topological cone of X. We say that a continuum X is cone-embeddable in Fn(X) if there is an embedding h from Cone(X) into Fn(X) such that h(x,0)={x} for each x in X. In this paper, we characterize trees X that are cone-embeddable in Fn(X).