  Black holes with planar or hyperbolic horizons are known to exist in AdS
space, alongside the usual ones with spherical horizons. In this paper, we
consider a one-parameter generalisation of these black holes that is contained
in the AdS C-metric. In terms of the domain-structure analysis recently
developed for such solutions, these black holes have a domain in the shape of a
triangle. It is shown that the horizons of these black holes are deformed
hyperbolic spaces, with the new parameter controlling the amount of
deformation. The space-times are static and completely regular outside the
horizons. We argue that these black holes are hyperbolic analogues of the
"slowly accelerating" spherical black holes known to exist in AdS space.
