  The discrete tensorial charges carried by orientifold planes define n-gerbes
in space-time. The simplest way to ensure a consistent string compactification
is to require these gerbes to be flat. This results in expressions for the
local gerbe-holonomies around each orientifold plane, describing its charges.
Inverting the procedure and considering all flat gerbes leads to a
classification of orientifold configurations. Requiring that the tadpole is
cancelled by adding D-branes, we classify all supersymmetric orientifolds on
T^k/Z_2 with 2^k O(9-k) planes at the fixed points, for k less or equal to 6.
For k=6 these theories organize in orbits of the SL(2,Z) S-duality symmetry of
N=4 supersymmetric gauge theories.
