# Monoclinic crystal system

An example of the monoclinic crystals, orthoclase

In crystallography, the monoclinic crystal system is one of the 7 crystal systems. 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 vectors are perpendicular (meet at right angles), while the third vector meets the other two at an angle other than 90°.

## Bravais lattices

Further information: Bravais lattice

### Two-dimensional

There is only one monoclinic Bravais lattice in two dimensions: the oblique lattice.

### Three-dimensional

Two monoclinic Bravais lattices exist: the primitive monoclinic and the centered monoclinic lattices.

Bravais lattice Primitive
monoclinic
Base-centered
monoclinic
Pearson symbol mP mS
Standard unit cell
Clinorhombic prism unit cell

In the monoclinic system there is a second choice of crystal axes that results in a unit cell with the shape of a clinorhombic prism,[1] although this axis setting is very rarely used; this is because the rectangular two-dimensional base layers can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices interchange in centering type.

## Crystal classes

The monoclinic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,[2] 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 [3] C2 2 22 [2]+ enantiomorphic polar
(halotrichite)
P2, P21
C2
6–9 Domatic [3] C1h (=C1v = Cs) 2 = m *11 [ ] polar
(hilgardite)
Pm, Pc
Cm, Cc
10–15 Prismatic [3] 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.