  We study event horizons of non-axisymmetric black holes and show how features
found in axisymmetric studies of colliding black holes and of toroidal black
holes are non-generic and how new features emerge. Most of the details of black
hole formation and black hole merger are known only in the axisymmetric case,
in which numerical evolution has successfully produced dynamical space-times.
The work that is presented here uses a new approach to construct the geometry
of the event horizon, not by locating it in a given spacetime, but by direct
construction. In the axisymmetric case, our method produces the familiar
pair-of-pants structure found in previous numerical simulations of black hole
mergers, as well as event horizons that go through a toroidal epoch as
discovered in the collapse of rotating matter. The main purpose of this paper
is to show how new - substantially different - features emerge in the
non-axisymmetric case. In particular, we show how black holes generically go
through a toroidal phase before they become spherical, and how this fits
together with the merger of black holes.
