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Fm-3m1' [#225.117] (Type: 2 -- Type II (grey group))

[OG: Fm-3m1' #225.2.1619]

Operators of Group 225.117 (Fm-3m1')

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,x,-z
0,0,0
( 
  0   1   0     0
  1   0   0     0
  0   0  -1     0
 )
2 x,x,0 +1 {2xy|0,0,0}
14.-y,-x,-z
0,0,0
( 
  0  -1   0     0
 -1   0   0     0
  0   0  -1     0
 )
2 x,-x,0 +1 {2-xy|0,0,0}
15.y,-x,z
0,0,0
( 
  0   1   0     0
 -1   0   0     0
  0   0   1     0
 )
4- 0,0,z +1 {4z-1|0,0,0}
16.-y,x,z
0,0,0
( 
  0  -1   0     0
  1   0   0     0
  0   0   1     0
 )
4+ 0,0,z +1 {4z|0,0,0}
17.x,z,-y
0,0,0
( 
  1   0   0     0
  0   0   1     0
  0  -1   0     0
 )
4- x,0,0 +1 {4x-1|0,0,0}
18.-x,z,y
0,0,0
( 
 -1   0   0     0
  0   0   1     0
  0   1   0     0
 )
2 0,y,y +1 {2yz|0,0,0}
19.-x,-z,-y
0,0,0
( 
 -1   0   0     0
  0   0  -1     0
  0  -1   0     0
 )
2 0,y,-y +1 {2-yz|0,0,0}
20.x,-z,y
0,0,0
( 
  1   0   0     0
  0   0  -1     0
  0   1   0     0
 )
4+ x,0,0 +1 {4x|0,0,0}
21.z,y,-x
0,0,0
( 
  0   0   1     0
  0   1   0     0
 -1   0   0     0
 )
4+ 0,y,0 +1 {4y|0,0,0}
22.z,-y,x
0,0,0
( 
  0   0   1     0
  0  -1   0     0
  1   0   0     0
 )
2 x,0,x +1 {2xz|0,0,0}
23.-z,y,x
0,0,0
( 
  0   0  -1     0
  0   1   0     0
  1   0   0     0
 )
4- 0,y,0 +1 {4y-1|0,0,0}
24.-z,-y,-x
0,0,0
( 
  0   0  -1     0
  0  -1   0     0
 -1   0   0     0
 )
2 -x,0,x +1 {2-xz|0,0,0}
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,-x,z
0,0,0
( 
  0  -1   0     0
 -1   0   0     0
  0   0   1     0
 )
m x,-x,z +1 {mxy|0,0,0}
38.y,x,z
0,0,0
( 
  0   1   0     0
  1   0   0     0
  0   0   1     0
 )
m x,x,z +1 {m-xy|0,0,0}
39.-y,x,-z
0,0,0
( 
  0  -1   0     0
  1   0   0     0
  0   0  -1     0
 )
-4- 0,0,z 0,0,0 +1 {-4z-1|0,0,0}
40.y,-x,-z
0,0,0
( 
  0   1   0     0
 -1   0   0     0
  0   0  -1     0
 )
-4+ 0,0,z 0,0,0 +1 {-4z|0,0,0}
41.-x,-z,y
0,0,0
( 
 -1   0   0     0
  0   0  -1     0
  0   1   0     0
 )
-4- x,0,0 0,0,0 +1 {-4x-1|0,0,0}
42.x,-z,-y
0,0,0
( 
  1   0   0     0
  0   0  -1     0
  0  -1   0     0
 )
m x,y,-y +1 {myz|0,0,0}
43.x,z,y
0,0,0
( 
  1   0   0     0
  0   0   1     0
  0   1   0     0
 )
m x,y,y +1 {m-yz|0,0,0}
44.-x,z,-y
0,0,0
( 
 -1   0   0     0
  0   0   1     0
  0  -1   0     0
 )
-4+ x,0,0 0,0,0 +1 {-4x|0,0,0}
45.-z,-y,x
0,0,0
( 
  0   0  -1     0
  0  -1   0     0
  1   0   0     0
 )
-4+ 0,y,0 0,0,0 +1 {-4y|0,0,0}
46.-z,y,-x
0,0,0
( 
  0   0  -1     0
  0   1   0     0
 -1   0   0     0
 )
m -x,y,x +1 {mxz|0,0,0}
47.z,-y,-x
0,0,0
( 
  0   0   1     0
  0  -1   0     0
 -1   0   0     0
 )
-4- 0,y,0 0,0,0 +1 {-4y-1|0,0,0}
48.z,y,x
0,0,0
( 
  0   0   1     0
  0   1   0     0
  1   0   0     0
 )
m x,y,x +1 {m-xz|0,0,0}
49.x,y+1/2,z+1/2
mx,my,mz
( 
  1   0   0     0
  0   1   0   1/2
  0   0   1   1/2
 )
t (0,1/2,1/2) +1 {1|0,1/2,1/2}
50d.-x,-y+1/2,z+1/2
-mx,-my,mz
( 
 -1   0   0     0
  0  -1   0   1/2
  0   0   1   1/2
 )
2 (0,0,1/2) 0,1/4,z +1 {2z|0,1/2,1/2}
51d.-x,y+1/2,-z+1/2
-mx,my,-mz
( 
 -1   0   0     0
  0   1   0   1/2
  0   0  -1   1/2
 )
2 (0,1/2,0) 0,y,1/4 +1 {2y|0,1/2,1/2}
52d.x,-y+1/2,-z+1/2
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0   1/2
  0   0  -1   1/2
 )
2 x,1/4,1/4 +1 {2x|0,1/2,1/2}
53d.z,x+1/2,y+1/2
mz,mx,my
( 
  0   0   1     0
  1   0   0   1/2
  0   1   0   1/2
 )
3+ (1/3,1/3,1/3) x-0.33333,x-1/6,x +1 {3xyz|0,1/2,1/2}
54d.z,-x+1/2,-y+1/2
mz,-mx,-my
( 
  0   0   1     0
 -1   0   0   1/2
  0  -1   0   1/2
 )
3+ -x,x+1/2,-x +1 {3x-yz-1|0,1/2,1/2}
55d.-z,-x+1/2,y+1/2
-mz,-mx,my
( 
  0   0  -1     0
 -1   0   0   1/2
  0   1   0   1/2
 )
3+ (-1/3,1/3,1/3) x+1/3,-x,-x +1 {3-xyz-1|0,1/2,1/2}
56d.-z,x+1/2,-y+1/2
-mz,mx,-my
( 
  0   0  -1     0
  1   0   0   1/2
  0  -1   0   1/2
 )
3+ -x,-x+1/2,x +1 {3xy-z-1|0,1/2,1/2}
57d.y,z+1/2,x+1/2
my,mz,mx
( 
  0   1   0     0
  0   0   1   1/2
  1   0   0   1/2
 )
3- (1/3,1/3,1/3) x-0.16666,x+1/6,x +1 {3xyz-1|0,1/2,1/2}
58d.-y,z+1/2,-x+1/2
-my,mz,-mx
( 
  0  -1   0     0
  0   0   1   1/2
 -1   0   0   1/2
 )
3- (-1/3,1/3,1/3) x+1/6,-x+1/6,-x +1 {3-xyz|0,1/2,1/2}
59d.y,-z+1/2,-x+1/2
my,-mz,-mx
( 
  0   1   0     0
  0   0  -1   1/2
 -1   0   0   1/2
 )
3- -x+1/2,-x+1/2,x +1 {3xy-z|0,1/2,1/2}
60d.-y,-z+1/2,x+1/2
-my,-mz,mx
( 
  0  -1   0     0
  0   0  -1   1/2
  1   0   0   1/2
 )
3- -x-1/2,x+1/2,-x +1 {3x-yz|0,1/2,1/2}
61d.y,x+1/2,-z+1/2
my,mx,-mz
( 
  0   1   0     0
  1   0   0   1/2
  0   0  -1   1/2
 )
2 (1/4,1/4,0) x,x+1/4,1/4 +1 {2xy|0,1/2,1/2}
62d.-y,-x+1/2,-z+1/2
-my,-mx,-mz
( 
  0  -1   0     0
 -1   0   0   1/2
  0   0  -1   1/2
 )
2 (-1/4,1/4,0) x,-x+1/4,1/4 +1 {2-xy|0,1/2,1/2}
63d.y,-x+1/2,z+1/2
my,-mx,mz
( 
  0   1   0     0
 -1   0   0   1/2
  0   0   1   1/2
 )
4- (0,0,1/2) 1/4,1/4,z +1 {4z-1|0,1/2,1/2}
64d.-y,x+1/2,z+1/2
-my,mx,mz
( 
  0  -1   0     0
  1   0   0   1/2
  0   0   1   1/2
 )
4+ (0,0,1/2) -1/4,1/4,z +1 {4z|0,1/2,1/2}
65d.x,z+1/2,-y+1/2
mx,mz,-my
( 
  1   0   0     0
  0   0   1   1/2
  0  -1   0   1/2
 )
4- x,1/2,0 +1 {4x-1|0,1/2,1/2}
66d.-x,z+1/2,y+1/2
-mx,mz,my
( 
 -1   0   0     0
  0   0   1   1/2
  0   1   0   1/2
 )
2 (0,1/2,1/2) 0,y,y +1 {2yz|0,1/2,1/2}
67d.-x,-z+1/2,-y+1/2
-mx,-mz,-my
( 
 -1   0   0     0
  0   0  -1   1/2
  0  -1   0   1/2
 )
2 0,y+1/2,-y +1 {2-yz|0,1/2,1/2}
68d.x,-z+1/2,y+1/2
mx,-mz,my
( 
  1   0   0     0
  0   0  -1   1/2
  0   1   0   1/2
 )
4+ x,0,1/2 +1 {4x|0,1/2,1/2}
69d.z,y+1/2,-x+1/2
mz,my,-mx
( 
  0   0   1     0
  0   1   0   1/2
 -1   0   0   1/2
 )
4+ (0,1/2,0) 1/4,y,1/4 +1 {4y|0,1/2,1/2}
70d.z,-y+1/2,x+1/2
mz,-my,mx
( 
  0   0   1     0
  0  -1   0   1/2
  1   0   0   1/2
 )
2 (1/4,0,1/4) x-0.25,1/4,x +1 {2xz|0,1/2,1/2}
71d.-z,y+1/2,x+1/2
-mz,my,mx
( 
  0   0  -1     0
  0   1   0   1/2
  1   0   0   1/2
 )
4- (0,1/2,0) -1/4,y,1/4 +1 {4y-1|0,1/2,1/2}
72d.-z,-y+1/2,-x+1/2
-mz,-my,-mx
( 
  0   0  -1     0
  0  -1   0   1/2
 -1   0   0   1/2
 )
2 (-1/4,0,1/4) -x+1/4,1/4,x +1 {2-xz|0,1/2,1/2}