  We introduce a new optimization problem regarding embeddings of a graph into
a Euclidean space and discuss its relation to the two, mutually dual,
optimizations problems introduced by Goering-Helmberg-Wappler. We prove that
the Laplace eigenvalue maximization problem of Goering et al is also dual to
our embedding optimization problem. We solve the optimization problems for
generalized polygons and graphs isomorphic to the one-skeltons of regular and
semi-regular polyhedra.
