Monoclinic crystal system

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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[edit]

Further information: Bravais lattice


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


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

Bravais lattice Primitive
Pearson symbol mP mS
Standard unit cell Monoclinic.svg Monoclinic-base-centered.svg
Clinorhombic prism unit cell Clinorhombic prismC.svg Clinorhombic prism.svg

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[edit]

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
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
P2, P21
6–9 Domatic [3] C1h (=C1v = Cs) 2 = m *11 [ ] polar
Pm, Pc
Cm, Cc
10–15 Prismatic [3] C2h 2/m 2* [2,2+] centrosymmetric
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.

See also[edit]


  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. ^ a b c "The 32 crystal classes". Retrieved 2009-07-08. 

Further reading[edit]