  A family of spherically symmetric, static and self--dual Lorentzian wormholes
is obtained in n--dimensional Einstein gravity. This class of solutions
includes the n--dimensional versions of the Schwarzschild black hole and the
spatial--Schwarzschild traversable wormhole. Using isotropic coordinates we
study the geometrical structure of the solution, and delineate the domains of
the free parameters for which wormhole, naked singular geometries and the
Schwarzschild black hole are obtained. It is shown that, in the lower
dimensional Einstein gravity without cosmological constant, we can not have
self--dual Lorentzian wormholes.
