(Bravais?) lattice with one angle equal 90

[donali_mambo]

I have seen in some books that the triclinic bravais lattice ( a≠b≠c , α≠β≠γ ) excludes explicitly the option that one angle equal 90°. For instance 90°≠α≠β≠γ=90°.

If I got the definition of α, β and γ correctly, it would be a primitive cell with a pair of parallel faces as rectangles, and rhoumbuses in the other two pairs.

The question is: Why this lattice is not included in the bravais lattices? Is possible to redefine the vectors, such that they turn into one of the Bravais lattices?

 

[M Quack]

A lattice with just one angle at 90 deg does not have a special symmetry (unlike a monoclinic lattice with two 90 deg angles).

Therefore the 90deg does not have any significance and would only be "accidental" rather than locked by the appearance of a symmetry operation.

You can see this from looking at the point groups for the triclinic and monoclinic space groups: As soon as
there is a 2-fold rotation axis or mirror plane or both you are in the monoclinic lattice with two 90deg angles.

http://en.wikipedia.org/wiki/List_of_space_groups