Triclinic and Monoclinic (2 and m) Space Groups

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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To the right of each space group is a listing of coordinate points. These are the coordinates to which a general point (x,y,z) is transformed by the space group. Origins (called "equivalent points" in the International Tables), are additional points around which the points are transformed. For example, (0,0,0) refers to a corner of the unit cell, (1/2,1/2,1/2) to the center. All space groups have origin (0,0,0). For a space group with an additional origin (1/2,1/2,1/2), point (x,y,z) is also transformed to (1/2+x,1/2+y,1/2+z) and so on.

The monoclinic space groups shown here are shown from two vantage points: one along the two-fold axes and one perpendicular to them. Coordinates are listed for both orientations.

Triclinic Space Groups

 1. P1 (x,y,z) 2.    P1' (x,y,z); (-x,-y,-z)

Monoclinic (2) Space Groups

The monoclinic space groups shown here are shown from two vantage points: one along the two-fold axes and one perpendicular to them. Coordinates are listed for both orientations.

 3. P2 (x,y,z); (-x,-y,z) P2 (x,y,z); (-x,y,-z) 4. P21 (x,y,z); (-x,-y,1/2+z) P21 (x,y,z); (-x,1/2+y,-z) 5. B2 (x,y,z); (-x,-y,z); Origins: (0,0,0); (1/2,0,1/2) C2 (x,y,z); (-x,y,-z); Origins: (0,0,0); (1/2,1/2,0)

Monoclinic (m) Space Groups

The monoclinic space groups shown here are shown from two vantage points: one along the two-fold axes and one perpendicular to them. Coordinates are listed for both orientations.

 6. Pm (x,y,z); (x,y,-z) Pm (x,y,z); (x,-y,z) 7. Pb (x,y,z); (x,1/2+y,-z) Pc (x,y,z); (x,-y,1/2+z) 8. Bm (x,y,z); (x,y,-z); Origins:(0,0,0); (1/2,0,1/2) Cm (x,y,z); (x,-y,z); Origins:(0,0,0),(1/2,1/2,0) 9. Bb(x,y,z); (x,1/2+y,-z); Origins:(0,0,0); (1/2,0,1/2) Cc (x,y,z); (x,-y,1/2+z); Origins:(0,0,0); (1/2,1/2,0)

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Created 30 March 1999, Last Update 15 December, 2011

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