Monoclinic crystal system
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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°.
Contents
Bravais lattices
Twodimensional
There is only one monoclinic Bravais lattice in two dimensions: the oblique lattice.
Threedimensional
Two monoclinic Bravais lattices exist: the primitive monoclinic and the basecentered monoclinic lattices.
Bravais lattice  Primitive monoclinic 
Basecentered monoclinic 

Pearson symbol  mP  mS 
Standard unit cell  
Oblique rhombic prism unit cell 
In the monoclinic system there is a rarely used second choice of crystal axes that results in a unit cell with the shape of an oblique rhombic prism;^{[1]} it can be constructed because the rectangular twodimensional base layer can also be described with rhombic axes. In this axis setting, the primitive and basecentered lattices swap in centering type.
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  Basecentered  
3–5  Sphenoidal  C_{2}  2  22  [2]^{+}  enantiomorphic polar  halotrichite  P2, P2_{1}  C2 
6–9  Domatic  C_{s} (C_{1h})  m  *11  [ ]  polar  hilgardite  Pm, Pc  Cm, Cc 
10–12  Prismatic  C_{2h}  2/m  2*  [2,2^{+}]  centrosymmetric  gypsum  P2/m, P2_{1}/m  C2/m 
13–15  P2/c, P2_{1}/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 crosssection 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
References
 ^ See Hahn (2002), p. 746, row mC, column Primitive, where the cell parameters are given as a1 = a2, α = β
 ^ Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 9781402049699.
 ^ "The 32 crystal classes". Retrieved 20180619.
Further reading
 Hurlbut, Cornelius S.; Klein, Cornelis (1985). Manual of Mineralogy (20th ed.). pp. 69–73. ISBN 0471805807.
 Hahn, Theo, ed. (2002). International Tables for Crystallography, Volume A: Space Group Symmetry. A (5th ed.). Berlin, New York: SpringerVerlag. doi:10.1107/97809553602060000100. ISBN 9780792365907.