  Isolated horizons that admit the Hopf bundle structure $H\rightarrow S_2$ are
investigated, however the null direction is allowed not to be tangent to the
bundle fibres. The geometry of such horizons is characterised by data set on a
topological two-dimensional sphere, singular at its poles. The horizon
equations induced by Einstein's equations are imposed. The existence of regular
extremal horizons satisfying the vacuum (with cosmological constant) equation
of extremality, obtained from singular solutions on the sphere is pointed out.
All horizons (with assumed topology and in the generic case) satisfying the
$\Lambda$ vacuum type D equation are derived. They are compared to the Killing
horizons contained in the accelerated Kerr-NUT-(Anti) de Sitter spacetimes.
Both families of horizons have the same dimension, but the problem of mutual
correspondence needs to be better understood. If the cosmological constant
takes special values determined by the other parameters the bundle fibers
become tangent to the null direction. As an additional but also important
result, spacetimes of the topology $H\times \mathbb{R}$ locally isometric to
the accelerated Kerr-NUT-(Anti) de Sitter spacetimes are constructed for every
value of the mass, Kerr, NUT parameters, the cosmological constant and the
acceleration. When the acceleration parameter is not zero, the conical
singularity can be removed whenever the NUT parameter does not vanish either.
