# Tetragonal (4*2m) 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.

 111      p4i2m  (+x,+y,+z); (-x,-y,+z); (-x,+y,-z); (+x,-y,-z) (-y,+x,-z); (+y,-x,-z); (+y,+x,+z); (-y,-x,+z) 112      p4i2c   (+x,+y,+z); (-x,-y,+z); (-x,+y, 1/2-z); (+x,-y, 1/2-z) (-y,+x,-z); (+y,-x,-z); (+y,+x, 1/2+z); (-y,-x, 1/2+z) 113      p4i21m (+x,+y,+z); (-x,-y,+z); (1/2-x, 1/2+y,-z); (1/2+x, 1/2-y,-z) (-y,+x,-z); (+y,-x,-z); (1/2+y, 1/2+x,+z); (1/2-y, 1/2-x,+z) 114      p4i21c (+x,+y,+z); (-x,-y,+z); (1/2-x, 1/2+y, 1/2-z); (1/2+x, 1/2-y, 1/2-z) (-y,+x,-z); (+y,-x,-z); (1/2+y, 1/2+x, 1/2+z); (1/2-y, 1/2-x, 1/2+z) 115      p4im2  (+x,+y,+z); (-x,-y,+z); (-x,+y,+z,); (+x,-y,+z) (-y,+x,-z); (+y,-x,-z); (+y,+x,-z); (-y,-x,-z) 116      p4ic2   (+x,+y,+z); (-x,-y,+z); (-x,+y, 1/2+z,); (+x,-y, 1/2+z) (-y,+x,-z); (+y,-x,-z); (+y,+x, 1/2-z); (-y,-x, 1/2-z) 117      p4ib2   (+x,+y,+z); (-x,-y,+z); (1/2-x, 1/2+y,+z,); (1/2+x, 1/2-y,+z) (-y,+x,-z); (+y,-x,-z); (1/2+y, 1/2+x,-z); (1/2-y, 1/2-x,-z) 118      p4in2   (+x,+y,+z); (-x,-y,+z); (1/2-x, 1/2+y, 1/2+z,); (1/2+x, 1/2-y, 1/2+z) (-y,+x,-z); (+y,-x,-z); (1/2+y, 1/2+x, 1/2-z); (1/2-y, 1/2-x, 1/2-z) 119      i4im2 Origins: (0,0,0);  (1/2,1/2,1/2) (+x,+y,+z); (-x,-y,+z); (-x,+y,+z,); (+x,-y,+z) (-y,+x,-z); (+y,-x,-z); (+y,+x,-z); (-y,-x,-z) 120      i4ic2 Origins: (0,0,0);  (1/2,1/2,1/2)   (+x,+y,+z); (-x,-y,+z); (-x,+y, 1/2+z,); (+x,-y, 1/2+z)(-y,+x,-z); (+y,-x,-z); (+y,+x, 1/2-z); (-y,-x, 1/2-z) 121      i4i2m Origins: (0,0,0);  (1/2,1/2,1/2) (+x,+y,+z); (-x,-y,+z); (-x,+y,-z); (+x,-y,-z) (-y,+x,-z); (+y,-x,-z); (+y,+x,+z); (-y,-x,+z) 122      i4i2d Origins: (0,0,0);  (1/2,1/2,1/2) (+x,+y,+z); (-x,-y,+z); (-x,1/2+y,1/4-z); (+x,1/2-y,1/4-z) (-y,+x,-z); (+y,-x,-z); (+y, 1/2+x, 1/4+z); (-y, 1/2-x, 1/4+z)