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...