  We show how a recently discovered black ring solution with a rotating
2-sphere can be turned into two new solutions of Einstein-Maxwell-dilaton
theory. The first is a four-dimensional solution describing a pair of
oppositely charged, extremal black holes--known as a black dihole--undergoing
uniform acceleration. The second is a five-dimensional solution describing a
pair of concentric, static extremal black rings carrying opposite dipole
charges--a so-called black di-ring. The properties of both solutions, which
turn out to be formally very similar, are analyzed in detail. We also present,
in an appendix, an accelerating version of the Zipoy-Voorhees solution in
four-dimensional Einstein gravity.
