Since two of the angles are 90 deg, the lattice type could be monoclinic and not triclinic.

If I recall this correctly, the convention is that alpha is the angle between b+c, beta is the angle between a+c, and gamma is tha angle between a+b. I believe the obtuse angle is used (the one > 90 deg).

I think that a=X and b=Y for orthonormal shapes, but of course that's not exactly the case for monoclinic and triclinic cases.

My personal opinion is that unless your simulating a known crystal with known unit cell data, you may be asking for trouble by using a triclinic lattice.