  Equilibrium states of black holes can be modelled by isolated horizons. If
the intrinsic geometry is spherical, they are called type I while if it is
axi-symmetric, they are called type II. The detailed theory of geometry of
\emph{quantum} type I horizons and the calculation of their entropy can be
generalized to type II, thereby including arbitrary distortions and rotations.
The leading term in entropy of large horizons is again given by 1/4th of the
horizon area for the \emph{same} value of the Barbero-Immirzi parameter as in
the type I case. Ideas and constructions underlying this extension are
summarized.
