  We present several new space-periodic solutions of the static vacuum Einstein
equations in higher dimensions, both with and without black holes, having
Kasner asymptotics. These latter solutions are referred to as gravitational
solitons. Further partially compactified solutions are also obtained by taking
appropriate quotients, and the topologies are computed explicitly in terms of
connected sums of products of spheres. In addition, it is shown that there is a
correspondence, via Wick rotation, between the spacelike slices of the solitons
and black hole solutions in one dimension less. As a corollary, the solitons
give rise to complete Ricci flat Riemannian manifolds of infinite topological
type and generic holonomy, in dimensions 4 and higher.
