Orthorhombic (2/m 2/m 2/m) Space Groups
(P Lattices)

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.

047-pmm.gif (2291 bytes)

47 Pmmm

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

048-pnn.gif (2253 bytes)

48 Pnnn

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

049-pccm.gif (2166 bytes)

49 Pccm

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

050-pban.gif (2468 bytes)

50 Pban

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

051-pmma.gif (2053 bytes)

51 Pmma

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

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

052-pnna.gif (1992 bytes)

52 Pnna

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

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

053-pmna.gif (2077 bytes)

53 Pmna

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

054-pcca.gif (2128 bytes)

54 Pcca

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

055-pbam.gif (2059 bytes)

55 Pbam

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

056-pccn.gif (2114 bytes)

56 Pccn

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

057-pbcm.gif (2112 bytes)

57 Pbcm

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

058-pnnm.gif (2011 bytes)

58 Pnnm

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

059-pmmn.gif (2102 bytes)

59 Pmmn

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

060-pbcn.gif (2151 bytes)

60 Pbcn

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

061-pbca.gif (2197 bytes)

61 Pbca

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

062-pnma.gif (2249 bytes)

62 Pnma

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

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Created 30 March 1999, Last Update 31 May 2020