# Triclinic and Monoclinic (2 and m) Space Groups

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay

To the right of each space group is a listing of coordinate points. These are thecoordinates to which a general point (x,y,z) is transformed by the space group. Origins(called "equivalent points" in the International Tables), areadditional points around which the points are transformed. For example, (0,0,0) refers toa 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 alsotransformed 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 thetwo-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 thetwo-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 thetwo-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)