# Why is the base-centered orthorhombic crystal lattice a unique crystal system?

I'm having difficulty understanding why the base-centered orthorhombic crystal system is a unique crystal system. When I draw two base-centered orthorhombic unit cells next to each other there appears to be a primitive crystal that is contained within the union of the two lattices as shown in the image below.

This primitive crystal system appears to be monoclinic--though I wouldn't be surprised if I'm wrong on that front--if you take δ to be the typical β angle of a monoclinic crystal system (I've set δ ≠ 120° to avoid the rhombohedral scenario). Why does this not make the base-centered orthorhombic lattice redundant? Am I misguided in trying to understand these crystal systems in terms of their lattice points and unit cell lengths instead of their symmetry?

Monoclinic lattices do not have their two oblique axes equal; or in terms of point group symmetry, the $$C_\mathrm{2h}$$ symmetry characteristic of monoclinic lattices is promoted to $$D_\mathrm{2h}$$, therefore orthorhombic, when those two axes are equal. Your primitive cell has what would be the two oblique axes of a monoclinic cell equal, therefore retaining the $$D_\mathrm{2h}$$ orthorhombic symmetry. Compare with this answer where a specific axis ratio turns an apparently tetragonal lattice into a cubic one.