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I am learning 7 crystal systems and 32 Bravais lattices.

I am quite confused about why a base-centered orthorhombic Bravais lattice is not a simple monoclinic one, if we take two edges and a half diagonal as basis?

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Because orthorhombic has a higher symmetry. Both orthorhombic and monoclinic have unit cells with unequal edge lengths ($a \ne b \ne c$). All of the unit cell angles are 90 degrees for orthorhombic ($\alpha = \beta = \gamma = 90^{\circ}$). However, for monoclinic, one of the angles is not $90^{\circ}$ - this reduces the symmetry of the crystal. While you might say then that orthorhombic is a special case of monoclinic, that special case results in a higher number of symmetries of the unit cell and the resulting Bravais lattices constructed with it.

No choice of basis will add the $\alpha = \beta = \gamma$ symmetry back into monoclinic to get to orthorhombic. They are fundamentally different point groups.

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