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

001-P1.GIF (820 bytes) 1. P1

(x,y,z)

002-pi.gif (1076 bytes) 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.

003-p2.gif (2169 bytes) 3. P2

(x,y,z); (-x,-y,z)

P2

(x,y,z); (-x,y,-z)

004-p2i.gif (2181 bytes) 4. P21

(x,y,z); (-x,-y,1/2+z)

P21

(x,y,z); (-x,1/2+y,-z)

005-b2.gif (2703 bytes) 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.

006-pm.gif (1793 bytes) 6. Pm

(x,y,z); (x,y,-z)

Pm

(x,y,z); (x,-y,z)

007-pb.gif (1870 bytes) 7. Pb

(x,y,z); (x,1/2+y,-z)

Pc

(x,y,z); (x,-y,1/2+z)

008-bm.gif (2223 bytes) 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)

009-bb.gif (2172 bytes) 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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