  We consider isolated horizons (Killing horizons up to the second order) whose
null flow has the structure of a U(1) principal fiber bundle over a compact
Riemann surface. We impose the vacuum Einstein equations (with the cosmological
constant) and the condition that the spacetime Weyl tensor is of Petrov D type
on the geometry of the horizons. We derive all the solutions in the case when
the genus of the surface is $>1$. By doing so for all the non-trivial bundles,
we complete the classification. We construct the embedding spacetimes and show
that they are locally isometric to the toroidal or hyperbolic generalization of
the Taub-NUT-(anti-) de Sitter spacetimes for horizons of genus $1$ or $>1$
respectively, after performing Misner's identification of the spacetime. The
horizon bundle structure can be naturally extended to bundle structure defined
on the entire spacetime.
