  The geometric operators of area, volume, and length, depend on a fundamental
length l of quantum geometry which is a priori arbitrary rather than equal to
the Planck length l_P. The fundamental length l and the Immirzi parameter
$\gamma$ determine each other. With any l the entropy formula is rendered most
naturally in units of the length gap sqrt{{sqrt 3}/2} (sqrt{gamma} l).
  Independently of the choice of l, the black hole entropy derived from quantum
geometry in the limit of classical geometry is completely consistent with the
Bekenstein-Hawking form.
  The extremal limit of 1-puncture states of the quantum surface geometry
corresponds rather to an extremal string than to a classical horizon.
