Monoclinic crystal system

In crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism with a parallelogram as base. Hence two pairs of vectors are perpendicular, while the third pair make an angle other than 90°.

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There exist two monoclinic Bravais lattices: the simple monoclinic and the centered monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.

The crystal classes that fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and mineral examples.

Name	International	Schoenflies	Example
monoclinic normal	$\frac2m$	C_2h	gypsum, orthoclase, mica
monoclinic hemimorphic	$2$	C₂	halotrichite
monoclinic hemihedral	$m$	C_1h	hilgardite

The number of space groups for each crystal class is 6, 3, and 4, respectively.

The three monoclinic hemimorphic space groups are as follows:

a prism with as cross-section wallpaper group p2
ditto with screw axes instead of axes
ditto with screw axes as well as axes, parallel, in between; in this case an additional translation vector is one half of a translation vector in the base plane plus one half of a perpendicular vector between the base planes

The four monoclinic hemihedral space groups include

those with pure reflection at the base of the prism and halfway
those with glide planes instead of pure reflection planes; the glide is one half of a translation vector in the base plane
those with both in between each other; in this case an additional translation vector is this glide plus one half of a perpendicular vector between the base planes.