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Pm-3n1' [#223.105] (Type: 2 -- Type II (grey group))

[OG: Pm-3n1' #223.2.1607]

Operators of Group 223.105 (Pm-3n1')

1.x,y,z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 )
1 +1 {1|0,0,0}
2.-x,-y,z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 )
2 0,0,z +1 {2z|0,0,0}
3.-x,y,-z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     0
 )
2 0,y,0 +1 {2y|0,0,0}
4.x,-y,-z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
2 x,0,0 +1 {2x|0,0,0}
5.z,x,y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0   1   0     0
 )
3+ x,x,x +1 {3xyz|0,0,0}
6.z,-x,-y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0  -1   0     0
 )
3+ -x,x,-x +1 {3x-yz-1|0,0,0}
7.-z,-x,y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0   1   0     0
 )
3+ x,-x,-x +1 {3-xyz-1|0,0,0}
8.-z,x,-y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0  -1   0     0
 )
3+ -x,-x,x +1 {3xy-z-1|0,0,0}
9.y,z,x
0,0,0
( 
  0   1   0     0
  0   0   1     0
  1   0   0     0
 )
3- x,x,x +1 {3xyz-1|0,0,0}
10.-y,z,-x
0,0,0
( 
  0  -1   0     0
  0   0   1     0
 -1   0   0     0
 )
3- x,-x,-x +1 {3-xyz|0,0,0}
11.y,-z,-x
0,0,0
( 
  0   1   0     0
  0   0  -1     0
 -1   0   0     0
 )
3- -x,-x,x +1 {3xy-z|0,0,0}
12.-y,-z,x
0,0,0
( 
  0  -1   0     0
  0   0  -1     0
  1   0   0     0
 )
3- -x,x,-x +1 {3x-yz|0,0,0}
13.y+1/2,x+1/2,-z+1/2
0,0,0
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2
 )
2 (1/2,1/2,0) x,x,1/4 +1 {2xy|1/2,1/2,1/2}
14.-y+1/2,-x+1/2,-z+1/2
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2
 )
2 x,-x+1/2,1/4 +1 {2-xy|1/2,1/2,1/2}
15.y+1/2,-x+1/2,z+1/2
0,0,0
( 
  0   1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2
 )
4- (0,0,1/2) 1/2,0,z +1 {4z-1|1/2,1/2,1/2}
16.-y+1/2,x+1/2,z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0   1/2
  0   0   1   1/2
 )
4+ (0,0,1/2) 0,1/2,z +1 {4z|1/2,1/2,1/2}
17.x+1/2,z+1/2,-y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2
 )
4- (1/2,0,0) x,1/2,0 +1 {4x-1|1/2,1/2,1/2}
18.-x+1/2,z+1/2,y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2
 )
2 (0,1/2,1/2) 1/4,y,y +1 {2yz|1/2,1/2,1/2}
19.-x+1/2,-z+1/2,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2
 )
2 1/4,y+1/2,-y +1 {2-yz|1/2,1/2,1/2}
20.x+1/2,-z+1/2,y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2
 )
4+ (1/2,0,0) x,0,1/2 +1 {4x|1/2,1/2,1/2}
21.z+1/2,y+1/2,-x+1/2
0,0,0
( 
  0   0   1   1/2
  0   1   0   1/2
 -1   0   0   1/2
 )
4+ (0,1/2,0) 1/2,y,0 +1 {4y|1/2,1/2,1/2}
22.z+1/2,-y+1/2,x+1/2
0,0,0
( 
  0   0   1   1/2
  0  -1   0   1/2
  1   0   0   1/2
 )
2 (1/2,0,1/2) x,1/4,x +1 {2xz|1/2,1/2,1/2}
23.-z+1/2,y+1/2,x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0   1/2
  1   0   0   1/2
 )
4- (0,1/2,0) 0,y,1/2 +1 {4y-1|1/2,1/2,1/2}
24.-z+1/2,-y+1/2,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
 -1   0   0   1/2
 )
2 -x+1/2,1/4,x +1 {2-xz|1/2,1/2,1/2}
25.-x,-y,-z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
-1 0,0,0 +1 {-1|0,0,0}
26.x,y,-z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0  -1     0
 )
m x,y,0 +1 {mz|0,0,0}
27.x,-y,z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0   1     0
 )
m x,0,z +1 {my|0,0,0}
28.-x,y,z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0   1     0
 )
m 0,y,z +1 {mx|0,0,0}
29.-z,-x,-y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0  -1   0     0
 )
-3+ x,x,x 0,0,0 +1 {-3xyz|0,0,0}
30.-z,x,y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0   1   0     0
 )
-3+ -x,x,-x 0,0,0 +1 {-3x-yz-1|0,0,0}
31.z,x,-y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0  -1   0     0
 )
-3+ x,-x,-x 0,0,0 +1 {-3-xyz-1|0,0,0}
32.z,-x,y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0   1   0     0
 )
-3+ -x,-x,x 0,0,0 +1 {-3xy-z-1|0,0,0}
33.-y,-z,-x
0,0,0
( 
  0  -1   0     0
  0   0  -1     0
 -1   0   0     0
 )
-3- x,x,x 0,0,0 +1 {-3xyz-1|0,0,0}
34.y,-z,x
0,0,0
( 
  0   1   0     0
  0   0  -1     0
  1   0   0     0
 )
-3- x,-x,-x 0,0,0 +1 {-3-xyz|0,0,0}
35.-y,z,x
0,0,0
( 
  0  -1   0     0
  0   0   1     0
  1   0   0     0
 )
-3- -x,-x,x 0,0,0 +1 {-3xy-z|0,0,0}
36.y,z,-x
0,0,0
( 
  0   1   0     0
  0   0   1     0
 -1   0   0     0
 )
-3- -x,x,-x 0,0,0 +1 {-3x-yz|0,0,0}
37.-y+1/2,-x+1/2,z+1/2
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2
 )
c x+1/2,-x,z +1 {mxy|1/2,1/2,1/2}
38.y+1/2,x+1/2,z+1/2
0,0,0
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0   1   1/2
 )
n (1/2,1/2,1/2) x,x,z +1 {m-xy|1/2,1/2,1/2}
39.-y+1/2,x+1/2,-z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2
 )
-4- 0,1/2,z 0,1/2,1/4 +1 {-4z-1|1/2,1/2,1/2}
40.y+1/2,-x+1/2,-z+1/2
0,0,0
( 
  0   1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2
 )
-4+ 1/2,0,z 1/2,0,1/4 +1 {-4z|1/2,1/2,1/2}
41.-x+1/2,-z+1/2,y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2
 )
-4- x,0,1/2 1/4,0,1/2 +1 {-4x-1|1/2,1/2,1/2}
42.x+1/2,-z+1/2,-y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2
 )
a x,y+1/2,-y +1 {myz|1/2,1/2,1/2}
43.x+1/2,z+1/2,y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2
 )
n (1/2,1/2,1/2) x,y,y +1 {m-yz|1/2,1/2,1/2}
44.-x+1/2,z+1/2,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2
 )
-4+ x,1/2,0 1/4,1/2,0 +1 {-4x|1/2,1/2,1/2}
45.-z+1/2,-y+1/2,x+1/2
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0   1/2
 )
-4+ 0,y,1/2 0,1/4,1/2 +1 {-4y|1/2,1/2,1/2}
46.-z+1/2,y+1/2,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0   1/2
 -1   0   0   1/2
 )
b -x+1/2,y,x +1 {mxz|1/2,1/2,1/2}
47.z+1/2,-y+1/2,-x+1/2
0,0,0
( 
  0   0   1   1/2
  0  -1   0   1/2
 -1   0   0   1/2
 )
-4- 1/2,y,0 1/2,1/4,0 +1 {-4y-1|1/2,1/2,1/2}
48.z+1/2,y+1/2,x+1/2
0,0,0
( 
  0   0   1   1/2
  0   1   0   1/2
  1   0   0   1/2
 )
n (1/2,1/2,1/2) x,y,x +1 {m-xz|1/2,1/2,1/2}
49.x,y,z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 ) '
1 -1 {1|0,0,0}'
50.-x,-y,z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 ) '
2 0,0,z -1 {2z|0,0,0}'
51.-x,y,-z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     0
 ) '
2 0,y,0 -1 {2y|0,0,0}'
52.x,-y,-z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     0
 ) '
2 x,0,0 -1 {2x|0,0,0}'
53.z,x,y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0   1   0     0
 ) '
3+ x,x,x -1 {3xyz|0,0,0}'
54.z,-x,-y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0  -1   0     0
 ) '
3+ -x,x,-x -1 {3x-yz-1|0,0,0}'
55.-z,-x,y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0   1   0     0
 ) '
3+ x,-x,-x -1 {3-xyz-1|0,0,0}'
56.-z,x,-y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0  -1   0     0
 ) '
3+ -x,-x,x -1 {3xy-z-1|0,0,0}'
57.y,z,x
0,0,0
( 
  0   1   0     0
  0   0   1     0
  1   0   0     0
 ) '
3- x,x,x -1 {3xyz-1|0,0,0}'
58.-y,z,-x
0,0,0
( 
  0  -1   0     0
  0   0   1     0
 -1   0   0     0
 ) '
3- x,-x,-x -1 {3-xyz|0,0,0}'
59.y,-z,-x
0,0,0
( 
  0   1   0     0
  0   0  -1     0
 -1   0   0     0
 ) '
3- -x,-x,x -1 {3xy-z|0,0,0}'
60.-y,-z,x
0,0,0
( 
  0  -1   0     0
  0   0  -1     0
  1   0   0     0
 ) '
3- -x,x,-x -1 {3x-yz|0,0,0}'
61.y+1/2,x+1/2,-z+1/2
0,0,0
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2
 ) '
2 (1/2,1/2,0) x,x,1/4 -1 {2xy|1/2,1/2,1/2}'
62.-y+1/2,-x+1/2,-z+1/2
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2
 ) '
2 x,-x+1/2,1/4 -1 {2-xy|1/2,1/2,1/2}'
63.y+1/2,-x+1/2,z+1/2
0,0,0
( 
  0   1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2
 ) '
4- (0,0,1/2) 1/2,0,z -1 {4z-1|1/2,1/2,1/2}'
64.-y+1/2,x+1/2,z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0   1/2
  0   0   1   1/2
 ) '
4+ (0,0,1/2) 0,1/2,z -1 {4z|1/2,1/2,1/2}'
65.x+1/2,z+1/2,-y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2
 ) '
4- (1/2,0,0) x,1/2,0 -1 {4x-1|1/2,1/2,1/2}'
66.-x+1/2,z+1/2,y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2
 ) '
2 (0,1/2,1/2) 1/4,y,y -1 {2yz|1/2,1/2,1/2}'
67.-x+1/2,-z+1/2,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2
 ) '
2 1/4,y+1/2,-y -1 {2-yz|1/2,1/2,1/2}'
68.x+1/2,-z+1/2,y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2
 ) '
4+ (1/2,0,0) x,0,1/2 -1 {4x|1/2,1/2,1/2}'
69.z+1/2,y+1/2,-x+1/2
0,0,0
( 
  0   0   1   1/2
  0   1   0   1/2
 -1   0   0   1/2
 ) '
4+ (0,1/2,0) 1/2,y,0 -1 {4y|1/2,1/2,1/2}'
70.z+1/2,-y+1/2,x+1/2
0,0,0
( 
  0   0   1   1/2
  0  -1   0   1/2
  1   0   0   1/2
 ) '
2 (1/2,0,1/2) x,1/4,x -1 {2xz|1/2,1/2,1/2}'
71.-z+1/2,y+1/2,x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0   1/2
  1   0   0   1/2
 ) '
4- (0,1/2,0) 0,y,1/2 -1 {4y-1|1/2,1/2,1/2}'
72.-z+1/2,-y+1/2,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
 -1   0   0   1/2
 ) '
2 -x+1/2,1/4,x -1 {2-xz|1/2,1/2,1/2}'
73.-x,-y,-z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 ) '
-1 0,0,0 -1 {-1|0,0,0}'
74.x,y,-z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0  -1     0
 ) '
m x,y,0 -1 {mz|0,0,0}'
75.x,-y,z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0   1     0
 ) '
m x,0,z -1 {my|0,0,0}'
76.-x,y,z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0   1     0
 ) '
m 0,y,z -1 {mx|0,0,0}'
77.-z,-x,-y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0  -1   0     0
 ) '
-3+ x,x,x 0,0,0 -1 {-3xyz|0,0,0}'
78.-z,x,y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0   1   0     0
 ) '
-3+ -x,x,-x 0,0,0 -1 {-3x-yz-1|0,0,0}'
79.z,x,-y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0  -1   0     0
 ) '
-3+ x,-x,-x 0,0,0 -1 {-3-xyz-1|0,0,0}'
80.z,-x,y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0   1   0     0
 ) '
-3+ -x,-x,x 0,0,0 -1 {-3xy-z-1|0,0,0}'
81.-y,-z,-x
0,0,0
( 
  0  -1   0     0
  0   0  -1     0
 -1   0   0     0
 ) '
-3- x,x,x 0,0,0 -1 {-3xyz-1|0,0,0}'
82.y,-z,x
0,0,0
( 
  0   1   0     0
  0   0  -1     0
  1   0   0     0
 ) '
-3- x,-x,-x 0,0,0 -1 {-3-xyz|0,0,0}'
83.-y,z,x
0,0,0
( 
  0  -1   0     0
  0   0   1     0
  1   0   0     0
 ) '
-3- -x,-x,x 0,0,0 -1 {-3xy-z|0,0,0}'
84.y,z,-x
0,0,0
( 
  0   1   0     0
  0   0   1     0
 -1   0   0     0
 ) '
-3- -x,x,-x 0,0,0 -1 {-3x-yz|0,0,0}'
85.-y+1/2,-x+1/2,z+1/2
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2
 ) '
c x+1/2,-x,z -1 {mxy|1/2,1/2,1/2}'
86.y+1/2,x+1/2,z+1/2
0,0,0
( 
  0   1   0   1/2
  1   0   0   1/2
  0   0   1   1/2
 ) '
n (1/2,1/2,1/2) x,x,z -1 {m-xy|1/2,1/2,1/2}'
87.-y+1/2,x+1/2,-z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2
 ) '
-4- 0,1/2,z 0,1/2,1/4 -1 {-4z-1|1/2,1/2,1/2}'
88.y+1/2,-x+1/2,-z+1/2
0,0,0
( 
  0   1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2
 ) '
-4+ 1/2,0,z 1/2,0,1/4 -1 {-4z|1/2,1/2,1/2}'
89.-x+1/2,-z+1/2,y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2
 ) '
-4- x,0,1/2 1/4,0,1/2 -1 {-4x-1|1/2,1/2,1/2}'
90.x+1/2,-z+1/2,-y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2
 ) '
a x,y+1/2,-y -1 {myz|1/2,1/2,1/2}'
91.x+1/2,z+1/2,y+1/2
0,0,0
( 
  1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2
 ) '
n (1/2,1/2,1/2) x,y,y -1 {m-yz|1/2,1/2,1/2}'
92.-x+1/2,z+1/2,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2
 ) '
-4+ x,1/2,0 1/4,1/2,0 -1 {-4x|1/2,1/2,1/2}'
93.-z+1/2,-y+1/2,x+1/2
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0   1/2
 ) '
-4+ 0,y,1/2 0,1/4,1/2 -1 {-4y|1/2,1/2,1/2}'
94.-z+1/2,y+1/2,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0   1/2
 -1   0   0   1/2
 ) '
b -x+1/2,y,x -1 {mxz|1/2,1/2,1/2}'
95.z+1/2,-y+1/2,-x+1/2
0,0,0
( 
  0   0   1   1/2
  0  -1   0   1/2
 -1   0   0   1/2
 ) '
-4- 1/2,y,0 1/2,1/4,0 -1 {-4y-1|1/2,1/2,1/2}'
96.z+1/2,y+1/2,x+1/2
0,0,0
( 
  0   0   1   1/2
  0   1   0   1/2
  1   0   0   1/2
 ) '
n (1/2,1/2,1/2) x,y,x -1 {m-xz|1/2,1/2,1/2}'


Go to the Wyckoff Positions of 223.105 (Pm-3n1')
Go to the extinction rules of 223.105 (Pm-3n1')


Back to the list of magnetic space groups derived from Pm-3n
Back to the list of Magnetic Space Groups

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