Orthorhombic (mm) Space Groups

Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof 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.

025-pmm2.gif (1671 bytes)
 25. Pmm2

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,z)
026pmc2i.gif (1623 bytes) 26. Pmc21

(x,y,z); (-x,y,z); (-x,-y,1/2+z); (x,-y,1/2+z)
027-pcc2.gif (1558 bytes) 27. Pcc2

(x,y,z); (-x,-y,z); (-x,y,1/2+z); (x,-y,1/2+z)
028-pma2.gif (1502 bytes) 28. Pma2

(x,y,z); (-x,-y,z); (1/2-x,y,z); (1/2+x,-y,z)
029pca2i.gif (1502 bytes) 29. Pca21

(x,y,z); (-x,-y,1/2+z); (1/2-x,y,1/2+z); (1/2+x,-y,z)
030-pnc2.gif (1606 bytes) 30. Pnc2

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

031pmn2i.gif (1469 bytes)
 31. Pmn21

(x,y,z); (-x,y,z); (1/2-x,-y,1/2+z); (1/2+x,-y,1/2+z)
032-pba2.gif (1532 bytes) 32. Pba2

(x,y,z); (-x,y,z); (1/2-x,1/2+y,z); (1/2+x,1/2-y,z)
033pna2i.gif (1567 bytes) 33. Pna21

(x,y,z); (-x,-y,1/2+z); (1/2-x,1/2+y,1/2+z); (1/2+x,1/2-y,z)
034-pnn2.gif (1542 bytes) 34. Pnn2

(x,y,z); (-x,-y,z); (1/2-x,1/2+y,1/2+z); (1/2+x,1/2-y,1/2+z)
035-cmm2.gif (2032 bytes) 35. Cmm2

(x,y,z); (-x,-y,z); (x,-y,-z); (-x,y,z);
Origins: (0,0,0); (1/2,1/2,0)
036cmc2i.gif (1991 bytes) 36. Cmc21

(x,y,z); (-x,y,z); (-x,-y,1/2+z); (x,-y,1/2+z);
Origins: (0,0,0); (1/2,1/2,1/2)
037-ccc2.gif (1900 bytes) 37. Ccc2

(x,y,z); (-x,-y,z); (-x,y,1/2+z); (-x,y,1/2+z);
Origins: (0,0,0); (1/2,1/2,1/2)
038-amm2.gif (2190 bytes) 38. Amm2

(x,y,z); (-x,-y,z); (x,-y,-z); (x,-y,z);
Origins: (0,0,0); (0,1/2,1/2)
039-abm2.gif (2150 bytes) 39. Abm2

(x,y,z); (-x,-y,z); (-x,1/2+y,z); (x,1/2-y,z);
Origins: (0,0,0); (0,1/2,1/2)
040-ama2.gif (1682 bytes) 40. Ama2

(x,y,z); (-x,-y,z); (1/2-x,y,z); (1/2+x,-y,z);
Origins: (0,0,0); (0,1/2,1/2)
041-aba2.gif (1858 bytes) 41. Aba2

(x,y,z); (-x,-y,z); (1/2-x,1/2+y,z); (1/2+x,1/2-y,z);
Origins: (0,0,0); (0,1/2,1/2)
042-fmm2.gif (2109 bytes) 42. Fmm2

(x,y,z); (-x,-y,z); (-x,y,z); (x,-y,z);
Origins: (0,0,0); (0,1/2,1/2); (1/2,0,1/2); (1/2,1/2,1/2)
043-fdd2.gif (2272 bytes) 43. Fdd2

(x,y,z); (-x,-y,z); (1/4-x,1/4+y,1/4+z); (1/4+x,1/4-y,1/4+z);
Origins: (0,0,0); (0,1/2,1/2); (1/2,0,1/2); (1/2,1/2,0)
044-imm2.gif (2013 bytes) 44. Imm2

(x,y,z); (-x,-y,z); (-x,y,z); (x,-y,z);
Origins: (0,0,0); (1/2,1/2,1/2)
045-iba2.gif (1905 bytes) 45. Iba2

(x,y,z); (-x,-y,z); (-x,y,1/2+z); (x,-y,1/2+z);
Origins: (0,0,0); (1/2,1/2,1/2)
046-ima2.gif (1757 bytes) 46. Ima2

(x,y,z); (-x,-y,z); (1/2-x,y,z); (1/2+x,-y,z);
Origins: (0,0,0); (1/2,1/2,1/2)

Return to Symmetry Index
Return to 3d-Space Groups Index
Return to Crustal Materials (Mineralogy-petrology) Index

Return to Professor Dutch's Home Page

Created 30 March 1999, Last Update 31 May 2020