##### LANGUAGES
modified on 17 March 2011 at 17:47 ••• 1,963 views

# I4 1/acd

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```group number                 = 142
group name                   =   I4_1/acd
crystal system               = Tetragonal
setting number               = 1
number of symmetry operators = 32

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

= 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 0.5
0.0 0.0 1.0 0.5

= operator 3 =
0.0 -1.0 0.0 0.0
1.0 0.0 0.0 0.5
0.0 0.0 1.0 0.25

= operator 4 =
0.0 1.0 0.0 0.5
-1.0 0.0 0.0 0.0
0.0 0.0 1.0 0.75

= operator 5 =
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.0
0.0 0.0 -1.0 0.25

= operator 6 =
1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.75

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

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

= operator 9 =
-1.0 0.0 0.0 0.0
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 0.25

= operator 10 =
1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.0
0.0 0.0 -1.0 0.75

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

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

= operator 13 =
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 14 =
-1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.5

= operator 15 =
0.0 -1.0 0.0 0.5
-1.0 0.0 0.0 0.0
0.0 0.0 1.0 0.25

= operator 16 =
0.0 1.0 0.0 0.0
1.0 0.0 0.0 0.5
0.0 0.0 1.0 0.75

= operator 17 =
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 18 =
-1.0 0.0 0.0 1.0
0.0 -1.0 0.0 1.0
0.0 0.0 1.0 1.0

= operator 19 =
0.0 -1.0 0.0 0.5
1.0 0.0 0.0 1.0
0.0 0.0 1.0 0.75

= operator 20 =
0.0 1.0 0.0 1.0
-1.0 0.0 0.0 0.5
0.0 0.0 1.0 1.25

= operator 21 =
-1.0 0.0 0.0 1.0
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 0.75

= operator 22 =
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 1.0
0.0 0.0 -1.0 1.25

= operator 23 =
0.0 1.0 0.0 1.0
1.0 0.0 0.0 1.0
0.0 0.0 -1.0 0.5

= operator 24 =
0.0 -1.0 0.0 0.5
-1.0 0.0 0.0 0.5
0.0 0.0 -1.0 1.0

= operator 25 =
-1.0 0.0 0.0 0.5
0.0 -1.0 0.0 1.0
0.0 0.0 -1.0 0.75

= operator 26 =
1.0 0.0 0.0 1.0
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 1.25

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

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

= operator 29 =
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 30 =
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.5
0.0 0.0 1.0 1.0

= operator 31 =
0.0 -1.0 0.0 1.0
-1.0 0.0 0.0 0.5
0.0 0.0 1.0 0.75

= operator 32 =
0.0 1.0 0.0 0.5
1.0 0.0 0.0 1.0
0.0 0.0 1.0 1.25
```
```group number                 = 142
group name                   =   I4_1/acd
crystal system               = Tetragonal
setting number               = 2
number of symmetry operators = 32

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

= 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 =
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 4 =
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 5 =
-1.0 0.0 0.0 0.5
0.0 1.0 0.0 0.0
0.0 0.0 -1.0 0.0

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

= operator 7 =
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 8 =
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 9 =
-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 10 =
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 11 =
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 12 =
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 13 =
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.0
0.0 0.0 1.0 0.0

= operator 14 =
-1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.5

= operator 15 =
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 16 =
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 17 =
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 18 =
-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 19 =
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 20 =
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 21 =
-1.0 0.0 0.0 1.0
0.0 1.0 0.0 0.5
0.0 0.0 -1.0 0.5

= operator 22 =
1.0 0.0 0.0 0.5
0.0 -1.0 0.0 0.5
0.0 0.0 -1.0 1.0

= operator 23 =
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 24 =
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 25 =
-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 26 =
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 27 =
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 28 =
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 29 =
1.0 0.0 0.0 1.0
0.0 -1.0 0.0 0.5
0.0 0.0 1.0 0.5

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

= operator 31 =
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 32 =
0.0 1.0 0.0 1.25
1.0 0.0 0.0 1.25
0.0 0.0 1.0 1.25
```