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modified on 17 March 2011 at 17:57 ••• 5,205 views

# Ia-3d

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```group number                 = 230
group name                   =      Ia-3d
crystal system               = Cubic
setting number               = 1
number of symmetry operators = 96

+x,+y,+z
-x+1/2,-y,+z+1/2
-x,+y+1/2,-z+1/2
+x+1/2,-y+1/2,-z
+z,+x,+y
+z+1/2,-x+1/2,-y
-z+1/2,-x,+y+1/2
-z,+x+1/2,-y+1/2
+y,+z,+x
-y,+z+1/2,-x+1/2
+y+1/2,-z+1/2,-x
-y+1/2,-z,+x+1/2
+y+3/4,+x+1/4,-z+1/4
-y+3/4,-x+3/4,-z+3/4
+y+1/4,-x+1/4,+z+3/4
-y+1/4,+x+3/4,+z+1/4
+x+3/4,+z+1/4,-y+1/4
-x+1/4,+z+3/4,+y+1/4
-x+3/4,-z+3/4,-y+3/4
+x+1/4,-z+1/4,+y+3/4
+z+3/4,+y+1/4,-x+1/4
+z+1/4,-y+1/4,+x+3/4
-z+1/4,+y+3/4,+x+1/4
-z+3/4,-y+3/4,-x+3/4
-x,-y,-z
+x+1/2,+y,-z+1/2
+x,-y+1/2,+z+1/2
-x+1/2,+y+1/2,+z
-z,-x,-y
-z+1/2,+x+1/2,+y
+z+1/2,+x,-y+1/2
+z,-x+1/2,+y+1/2
-y,-z,-x
+y,-z+1/2,+x+1/2
-y+1/2,+z+1/2,+x
+y+1/2,+z,-x+1/2
-y+1/4,-x+3/4,+z+3/4
+y+1/4,+x+1/4,+z+1/4
-y+3/4,+x+3/4,-z+1/4
+y+3/4,-x+1/4,-z+3/4
-x+1/4,-z+3/4,+y+3/4
+x+3/4,-z+1/4,-y+3/4
+x+1/4,+z+1/4,+y+1/4
-x+3/4,+z+3/4,-y+1/4
-z+1/4,-y+3/4,+x+3/4
-z+3/4,+y+3/4,-x+1/4
+z+3/4,-y+1/4,-x+3/4
+z+1/4,+y+1/4,+x+1/4
+x+1/2,+y+1/2,+z+1/2
-x+1,-y+1/2,+z+1
-x+1/2,+y+1,-z+1
+x+1,-y+1,-z+1/2
+z+1/2,+x+1/2,+y+1/2
+z+1,-x+1,-y+1/2
-z+1,-x+1/2,+y+1
-z+1/2,+x+1,-y+1
+y+1/2,+z+1/2,+x+1/2
-y+1/2,+z+1,-x+1
+y+1,-z+1,-x+1/2
-y+1,-z+1/2,+x+1
+y+5/4,+x+3/4,-z+3/4
-y+5/4,-x+5/4,-z+5/4
+y+3/4,-x+3/4,+z+5/4
-y+3/4,+x+5/4,+z+3/4
+x+5/4,+z+3/4,-y+3/4
-x+3/4,+z+5/4,+y+3/4
-x+5/4,-z+5/4,-y+5/4
+x+3/4,-z+3/4,+y+5/4
+z+5/4,+y+3/4,-x+3/4
+z+3/4,-y+3/4,+x+5/4
-z+3/4,+y+5/4,+x+3/4
-z+5/4,-y+5/4,-x+5/4
-x+1/2,-y+1/2,-z+1/2
+x+1,+y+1/2,-z+1
+x+1/2,-y+1,+z+1
-x+1,+y+1,+z+1/2
-z+1/2,-x+1/2,-y+1/2
-z+1,+x+1,+y+1/2
+z+1,+x+1/2,-y+1
+z+1/2,-x+1,+y+1
-y+1/2,-z+1/2,-x+1/2
+y+1/2,-z+1,+x+1
-y+1,+z+1,+x+1/2
+y+1,+z+1/2,-x+1
-y+3/4,-x+5/4,+z+5/4
+y+3/4,+x+3/4,+z+3/4
-y+5/4,+x+5/4,-z+3/4
+y+5/4,-x+3/4,-z+5/4
-x+3/4,-z+5/4,+y+5/4
+x+5/4,-z+3/4,-y+5/4
+x+3/4,+z+3/4,+y+3/4
-x+5/4,+z+5/4,-y+3/4
-z+3/4,-y+5/4,+x+5/4
-z+5/4,+y+5/4,-x+3/4
+z+5/4,-y+3/4,-x+5/4
+z+3/4,+y+3/4,+x+3/4

= operator 1 =
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0

= operator 2 =
-1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.0
0.0 0.0 1.0 0.5

= operator 3 =
-1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 0.5

= operator 4 =
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.0

= operator 5 =
0.0 0.0 1.0 0.0
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0

= operator 6 =
0.0 0.0 1.0 0.5
-1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.0

= operator 7 =
0.0 0.0 -1.0 0.5
-1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.5

= operator 8 =
0.0 0.0 -1.0 0.0
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.5

= operator 9 =
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0
1.0 0.0 0.0 0.0

= operator 10 =
0.0 -1.0 0.0 0.0
0.0 0.0 1.0 0.5
-1.0 0.0 0.0 0.5

= operator 11 =
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 0.5
-1.0 0.0 0.0 0.0

= operator 12 =
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.0
1.0 0.0 0.0 0.5

= operator 13 =
0.0 1.0 0.0 0.75
1.0 0.0 0.0 0.25
0.0 0.0 -1.0 0.25

= operator 14 =
0.0 -1.0 0.0 0.75
-1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.75

= operator 15 =
0.0 1.0 0.0 0.25
-1.0 0.0 0.0 0.25
0.0 0.0 1.0 0.75

= operator 16 =
0.0 -1.0 0.0 0.25
1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.25

= operator 17 =
1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.25
0.0 -1.0 0.0 0.25

= operator 18 =
-1.0 0.0 0.0 0.25
0.0 0.0 1.0 0.75
0.0 1.0 0.0 0.25

= operator 19 =
-1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.75
0.0 -1.0 0.0 0.75

= operator 20 =
1.0 0.0 0.0 0.25
0.0 0.0 -1.0 0.25
0.0 1.0 0.0 0.75

= operator 21 =
0.0 0.0 1.0 0.75
0.0 1.0 0.0 0.25
-1.0 0.0 0.0 0.25

= operator 22 =
0.0 0.0 1.0 0.25
0.0 -1.0 0.0 0.25
1.0 0.0 0.0 0.75

= operator 23 =
0.0 0.0 -1.0 0.25
0.0 1.0 0.0 0.75
1.0 0.0 0.0 0.25

= operator 24 =
0.0 0.0 -1.0 0.75
0.0 -1.0 0.0 0.75
-1.0 0.0 0.0 0.75

= operator 25 =
-1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.0
0.0 0.0 -1.0 0.0

= operator 26 =
1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.0
0.0 0.0 -1.0 0.5

= operator 27 =
1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.5
0.0 0.0 1.0 0.5

= operator 28 =
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.5
0.0 0.0 1.0 0.0

= operator 29 =
0.0 0.0 -1.0 0.0
-1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.0

= operator 30 =
0.0 0.0 -1.0 0.5
1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.0

= operator 31 =
0.0 0.0 1.0 0.5
1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.5

= operator 32 =
0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.5

= operator 33 =
0.0 -1.0 0.0 0.0
0.0 0.0 -1.0 0.0
-1.0 0.0 0.0 0.0

= operator 34 =
0.0 1.0 0.0 0.0
0.0 0.0 -1.0 0.5
1.0 0.0 0.0 0.5

= operator 35 =
0.0 -1.0 0.0 0.5
0.0 0.0 1.0 0.5
1.0 0.0 0.0 0.0

= operator 36 =
0.0 1.0 0.0 0.5
0.0 0.0 1.0 0.0
-1.0 0.0 0.0 0.5

= operator 37 =
0.0 -1.0 0.0 0.25
-1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.75

= operator 38 =
0.0 1.0 0.0 0.25
1.0 0.0 0.0 0.25
0.0 0.0 1.0 0.25

= operator 39 =
0.0 -1.0 0.0 0.75
1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.25

= operator 40 =
0.0 1.0 0.0 0.75
-1.0 0.0 0.0 0.25
0.0 0.0 -1.0 0.75

= operator 41 =
-1.0 0.0 0.0 0.25
0.0 0.0 -1.0 0.75
0.0 1.0 0.0 0.75

= operator 42 =
1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.25
0.0 -1.0 0.0 0.75

= operator 43 =
1.0 0.0 0.0 0.25
0.0 0.0 1.0 0.25
0.0 1.0 0.0 0.25

= operator 44 =
-1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.75
0.0 -1.0 0.0 0.25

= operator 45 =
0.0 0.0 -1.0 0.25
0.0 -1.0 0.0 0.75
1.0 0.0 0.0 0.75

= operator 46 =
0.0 0.0 -1.0 0.75
0.0 1.0 0.0 0.75
-1.0 0.0 0.0 0.25

= operator 47 =
0.0 0.0 1.0 0.75
0.0 -1.0 0.0 0.25
-1.0 0.0 0.0 0.75

= operator 48 =
0.0 0.0 1.0 0.25
0.0 1.0 0.0 0.25
1.0 0.0 0.0 0.25

= operator 49 =
1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.5
0.0 0.0 1.0 0.5

= operator 50 =
-1.0 0.0 0.0 1.0
0.0 -1.0 0.0 0.5
0.0 0.0 1.0 1.0

= operator 51 =
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 1.0
0.0 0.0 -1.0 1.0

= operator 52 =
1.0 0.0 0.0 1.0
0.0 -1.0 0.0 1.0
0.0 0.0 -1.0 0.5

= operator 53 =
0.0 0.0 1.0 0.5
1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.5

= operator 54 =
0.0 0.0 1.0 1.0
-1.0 0.0 0.0 1.0
0.0 -1.0 0.0 0.5

= operator 55 =
0.0 0.0 -1.0 1.0
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 1.0

= operator 56 =
0.0 0.0 -1.0 0.5
1.0 0.0 0.0 1.0
0.0 -1.0 0.0 1.0

= operator 57 =
0.0 1.0 0.0 0.5
0.0 0.0 1.0 0.5
1.0 0.0 0.0 0.5

= operator 58 =
0.0 -1.0 0.0 0.5
0.0 0.0 1.0 1.0
-1.0 0.0 0.0 1.0

= operator 59 =
0.0 1.0 0.0 1.0
0.0 0.0 -1.0 1.0
-1.0 0.0 0.0 0.5

= operator 60 =
0.0 -1.0 0.0 1.0
0.0 0.0 -1.0 0.5
1.0 0.0 0.0 1.0

= operator 61 =
0.0 1.0 0.0 1.25
1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.75

= operator 62 =
0.0 -1.0 0.0 1.25
-1.0 0.0 0.0 1.25
0.0 0.0 -1.0 1.25

= operator 63 =
0.0 1.0 0.0 0.75
-1.0 0.0 0.0 0.75
0.0 0.0 1.0 1.25

= operator 64 =
0.0 -1.0 0.0 0.75
1.0 0.0 0.0 1.25
0.0 0.0 1.0 0.75

= operator 65 =
1.0 0.0 0.0 1.25
0.0 0.0 1.0 0.75
0.0 -1.0 0.0 0.75

= operator 66 =
-1.0 0.0 0.0 0.75
0.0 0.0 1.0 1.25
0.0 1.0 0.0 0.75

= operator 67 =
-1.0 0.0 0.0 1.25
0.0 0.0 -1.0 1.25
0.0 -1.0 0.0 1.25

= operator 68 =
1.0 0.0 0.0 0.75
0.0 0.0 -1.0 0.75
0.0 1.0 0.0 1.25

= operator 69 =
0.0 0.0 1.0 1.25
0.0 1.0 0.0 0.75
-1.0 0.0 0.0 0.75

= operator 70 =
0.0 0.0 1.0 0.75
0.0 -1.0 0.0 0.75
1.0 0.0 0.0 1.25

= operator 71 =
0.0 0.0 -1.0 0.75
0.0 1.0 0.0 1.25
1.0 0.0 0.0 0.75

= operator 72 =
0.0 0.0 -1.0 1.25
0.0 -1.0 0.0 1.25
-1.0 0.0 0.0 1.25

= operator 73 =
-1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.5

= operator 74 =
1.0 0.0 0.0 1.0
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 1.0

= operator 75 =
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 1.0
0.0 0.0 1.0 1.0

= operator 76 =
-1.0 0.0 0.0 1.0
0.0 1.0 0.0 1.0
0.0 0.0 1.0 0.5

= operator 77 =
0.0 0.0 -1.0 0.5
-1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.5

= operator 78 =
0.0 0.0 -1.0 1.0
1.0 0.0 0.0 1.0
0.0 1.0 0.0 0.5

= operator 79 =
0.0 0.0 1.0 1.0
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 1.0

= operator 80 =
0.0 0.0 1.0 0.5
-1.0 0.0 0.0 1.0
0.0 1.0 0.0 1.0

= operator 81 =
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.5
-1.0 0.0 0.0 0.5

= operator 82 =
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 1.0
1.0 0.0 0.0 1.0

= operator 83 =
0.0 -1.0 0.0 1.0
0.0 0.0 1.0 1.0
1.0 0.0 0.0 0.5

= operator 84 =
0.0 1.0 0.0 1.0
0.0 0.0 1.0 0.5
-1.0 0.0 0.0 1.0

= operator 85 =
0.0 -1.0 0.0 0.75
-1.0 0.0 0.0 1.25
0.0 0.0 1.0 1.25

= operator 86 =
0.0 1.0 0.0 0.75
1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.75

= operator 87 =
0.0 -1.0 0.0 1.25
1.0 0.0 0.0 1.25
0.0 0.0 -1.0 0.75

= operator 88 =
0.0 1.0 0.0 1.25
-1.0 0.0 0.0 0.75
0.0 0.0 -1.0 1.25

= operator 89 =
-1.0 0.0 0.0 0.75
0.0 0.0 -1.0 1.25
0.0 1.0 0.0 1.25

= operator 90 =
1.0 0.0 0.0 1.25
0.0 0.0 -1.0 0.75
0.0 -1.0 0.0 1.25

= operator 91 =
1.0 0.0 0.0 0.75
0.0 0.0 1.0 0.75
0.0 1.0 0.0 0.75

= operator 92 =
-1.0 0.0 0.0 1.25
0.0 0.0 1.0 1.25
0.0 -1.0 0.0 0.75

= operator 93 =
0.0 0.0 -1.0 0.75
0.0 -1.0 0.0 1.25
1.0 0.0 0.0 1.25

= operator 94 =
0.0 0.0 -1.0 1.25
0.0 1.0 0.0 1.25
-1.0 0.0 0.0 0.75

= operator 95 =
0.0 0.0 1.0 1.25
0.0 -1.0 0.0 0.75
-1.0 0.0 0.0 1.25

= operator 96 =
0.0 0.0 1.0 0.75
0.0 1.0 0.0 0.75
1.0 0.0 0.0 0.75
```