Monoclinic crystal system

In crystallography, the monoclinic crystal system is one of the seven 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 parallelogram prism. Hence two pairs of vectors are perpendicular (meet at right angles), while the third pair makes an angle other than 90°.

Monoclinic crystal
An example of the monoclinic crystal orthoclase

Bravais lattices

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

Bravais lattice Primitive
Pearson symbol mP mS
Unit cell

For the base-centered monoclinic lattice, the primitive cell has the shape of an oblique rhombic prism;[1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length of the primitive cell below equals of the conventional cell above.

Oblique rhombic prism primitive cell
Primitive cell of the base-centered monoclinic lattice
Relationship between base layers of primitive and conventional cells

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,[2] 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.

# Point group Type Example Space groups
Name[3] Schön. Intl Orb. Cox. Primitive Base-centered
3–5 Sphenoidal C2 2 22 [2]+ enantiomorphic polar halotrichite P2, P21 C2
6–9 Domatic Cs (C1h) m *11 [ ] polar hilgardite Pm, Pc Cm, Cc
10–12 Prismatic C2h 2/m 2* [2,2+] centrosymmetric gypsum P2/m, P21/m C2/m
13–15 P2/c, P21/c C2/c

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 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.

In two dimensions

The only monoclinic Bravais lattice in two dimensions is the oblique lattice.

Bravais lattice Oblique
Pearson symbol mp
Unit cell

See also


  1. See Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
  2. Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9.
  3. "The 32 crystal classes". Retrieved 2018-06-19.

Further reading

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