Monoclinic crystal system
One of the 7 crystal systems in crystallography
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Through Euclidean vector, Crystal and Parallelogram
Bravais lattices
Two monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic.
The body-centered and face-centered monoclinic lattices are equivalent to the base-centered monoclinic lattice with different choice of axes, while the B side-centered monoclinic lattice (with centerings on the parallelogram faces) is equivalent to the primitive monoclinic lattice with different choice of axes.
The primitive cell of the base-centered monoclinic lattice has the shape of an oblique rhombic prism; it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. The length a of the primitive cell below equals 1/2√(a2 + b2) of the conventional cell above.
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Crystal classes
The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers, followed by the crystal class name, its point group in Schoenflies notation, Hermann–Mauguin (international) notation, orbifold notation, and Coxeter notation, type descriptors, mineral examples, and the notation for the space groups.
Sphenoidal is also called monoclinic hemimorphic, domatic is also called monoclinic hemihedral, and prismatic is also called monoclinic normal.
The three monoclinic hemimorphic space groups are as follows:
- a prism with a wallpaper group p2 cross-section
- 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.
In two dimensions
The only monoclinic Bravais lattice in two dimensions is the oblique lattice.