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# Monoclinic

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 Title: Monoclinic Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Monoclinic

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 its base. Hence two pairs of vectors are perpendicular, while the third pair makes an angle other than 90°.

## Bravais lattices and point/space groups

Two monoclinic Bravais lattices exist: the primitive monoclinic and the centered monoclinic lattices, with layers with a rectangular and rhombic lattice, respectively.

Monoclinic Bravais lattice
Primitive (P) Base-centered (C)

## Crystal classes

The monoclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number, orbifold, type, and space groups are listed in the table below.

# Point group Example Type Space groups
Name Schönflies Intl orbifold Coxeter
3-5 monoclinic  C2 $2\$ 22 + halotrichite enantiomorphic polar $\mathrm\left\{P\right\}2\,\!$ $\mathrm\left\{P\right\}2_\left\{1\right\}\,\!$ $\mathrm\left\{C\right\}2\,\!$
6-9 Domatic  C1h (=C1v = Cs) $\bar\left\{2\right\} = m$ *11 [ ] hilgardite polar $\mathrm\left\{Pm\right\}\,\!$ $\mathrm\left\{Pc\right\}\,\!$ $\mathrm\left\{Cm\right\}\,\!$ $\mathrm\left\{Cc\right\}\,\!$
10-15 Prismatic  C2h $2/m\,\!$ 2* [2,2+] gypsum centrosymmetric $\mathrm\left\{P\right\}2/\mathrm\left\{m\right\}\,\!$ $\mathrm\left\{P\right\}2_\left\{1\right\}/\mathrm\left\{m\right\}\,\!$ $\mathrm\left\{C\right\}2/\mathrm\left\{m\right\}\,\!$ $\mathrm\left\{P\right\}2/\mathrm\left\{c\right\}\,\!$ $\mathrm\left\{P\right\}2_\left\{1\right\}/\mathrm\left\{c\right\}\,\!$ $\mathrm\left\{C\right\}2/\mathrm\left\{c\right\}\,\!$

Sphenoidal is also monoclinic hemimorphic; Domatic is also monoclinic hemihedral; Prismatic is also monoclinic normal.

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.

## Specific chemical examples

An example of a monoclinic crystal is elemental sulfur (which can also occur in a rhombic form).