  The algebra A(D-3)+++ dimensionally reduces to the E(D-1) symmetry algebra of
(12-D)-dimensional supergravity. An infinite set of five-dimensional
gravitational objects trivially embedded in D-dimensions is constructed by
identifying the null geodesic motion on cosets embedded in the generalised
Kac-Moody algebra A(D-3)+++. By analogy with supergravity these are bound
states of dual gravitons. The metric interpolates continuously between exotic
gravitational solutions generated by the action of the Geroch group but is not
a continuously transforming solution of the Einstein-Hilbert action. We
investigate mixed-symmetry fields in the brane sigma model, identify actions
for the full interpolating bound state and understand the obstruction to the
bound state being a solution of the Einstein-Hilbert action.
