# Monoclinic crystal system

An example of the monoclinic crystals, orthoclase

In crystallography, the monoclinic crystal system is one of the seven lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base. Hence two pairs of vectors are perpendicular (meet at right angles), 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
Name Primitive Base-centered
Pearson symbol mP mC
Unit cell

## Crystal classes

The monoclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,[1] orbifold, type, and space groups are listed in the table below.

# Point group Type
(Example)
Space groups
Name Schoenflies notation (Schön.) Hermann–Mauguin notation (Intl) orbifold (Orb.) Coxeter notation (Cox.)
3–5 Sphenoidal [2] C2 $2\$ 22 [2]+ enantiomorphic polar
(halotrichite)
P2, P21
C2
6–9 Domatic [2] C1h (=C1v = Cs) $\bar{2} = m$ *11 [ ] polar
(hilgardite)
Pm, Pc
Cm, Cc
10–15 Prismatic [2] C2h $2/m\,\!$ 2* [2,2+] centrosymmetric
(gypsum)
P2/m, P21/m, C2/m
P2/c, P21/c, C2/c

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).[3]