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General Positions of the Group Pc6/mcc (#192.252) [BNS setting]


To display the general positions in the OG setting, please follow this link: P2c6/mm'm' ( #191.13.1475) [Transformation matrix]

Translation lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1|0,0,0)

Black-and-white lattice generators: (1|1,0,0), (1|0,1,0), (1|0,0,1), (1'|0,0,1/2)

N Standard/Default Setting
(x,y,z) form Matrix form Geom. interp. Seitz notation
1 x, y, z, +1
mx,my,mz
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
1 +1 { 1 | 0 }
2 x-y, x, z, +1
mx-my,mx,mz
(
   1  -1   0    0
   1   0   0    0
   0   0   1    0
)
6+ 0,0,z +1 { 6+001 | 0 }
3 -y, x-y, z, +1
-my,mx-my,mz
(
   0  -1   0    0
   1  -1   0    0
   0   0   1    0
)
3+ 0,0,z +1 { 3+001 | 0 }
4 -x, -y, z, +1
-mx,-my,mz
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z +1 { 2001 | 0 }
5 -x+y, -x, z, +1
-mx+my,-mx,mz
(
  -1   1   0    0
  -1   0   0    0
   0   0   1    0
)
3- 0,0,z +1 { 3-001 | 0 }
6 y, -x+y, z, +1
my,-mx+my,mz
(
   0   1   0    0
  -1   1   0    0
   0   0   1    0
)
6- 0,0,z +1 { 6-001 | 0 }
7 x-y, -y, -z+1/2, +1
mx-my,-my,-mz
(
   1  -1   0    0
   0  -1   0    0
   0   0  -1   1/2
)
2 x,0,1/4 +1 { 2100 | 0 0 1/2 }
8 y, x, -z+1/2, +1
my,mx,-mz
(
   0   1   0    0
   1   0   0    0
   0   0  -1   1/2
)
2 x,x,1/4 +1 { 2110 | 0 0 1/2 }
9 -x, -x+y, -z+1/2, +1
-mx,-mx+my,-mz
(
  -1   0   0    0
  -1   1   0    0
   0   0  -1   1/2
)
2 0,y,1/4 +1 { 2010 | 0 0 1/2 }
10 x, x-y, -z+1/2, +1
mx,mx-my,-mz
(
   1   0   0    0
   1  -1   0    0
   0   0  -1   1/2
)
2 2x,x,1/4 +1 { 2210 | 0 0 1/2 }
11 -x+y, y, -z+1/2, +1
-mx+my,my,-mz
(
  -1   1   0    0
   0   1   0    0
   0   0  -1   1/2
)
2 x,2x,1/4 +1 { 2120 | 0 0 1/2 }
12 -y, -x, -z+1/2, +1
-my,-mx,-mz
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1   1/2
)
2 x,-x,1/4 +1 { 21-10 | 0 0 1/2 }
13 -x, -y, -z, +1
mx,my,mz
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 +1 { -1 | 0 }
14 -x+y, -x, -z, +1
mx-my,mx,mz
(
  -1   1   0    0
  -1   0   0    0
   0   0  -1    0
)
-6+ 0,0,z 0,0,0 +1 { -6+001 | 0 }
15 y, -x+y, -z, +1
-my,mx-my,mz
(
   0   1   0    0
  -1   1   0    0
   0   0  -1    0
)
-3+ 0,0,z 0,0,0 +1 { -3+001 | 0 }
16 x, y, -z, +1
-mx,-my,mz
(
   1   0   0    0
   0   1   0    0
   0   0  -1    0
)
m x,y,0 +1 { m001 | 0 }
17 x-y, x, -z, +1
-mx+my,-mx,mz
(
   1  -1   0    0
   1   0   0    0
   0   0  -1    0
)
-3- 0,0,z 0,0,0 +1 { -3-001 | 0 }
18 -y, x-y, -z, +1
my,-mx+my,mz
(
   0  -1   0    0
   1  -1   0    0
   0   0  -1    0
)
-6- 0,0,z 0,0,0 +1 { -6-001 | 0 }
19 -x+y, y, z+1/2, +1
mx-my,-my,-mz
(
  -1   1   0    0
   0   1   0    0
   0   0   1   1/2
)
c x,2x,z +1 { m100 | 0 0 1/2 }
20 -y, -x, z+1/2, +1
my,mx,-mz
(
   0  -1   0    0
  -1   0   0    0
   0   0   1   1/2
)
c x,-x,z +1 { m110 | 0 0 1/2 }
21 x, x-y, z+1/2, +1
-mx,-mx+my,-mz
(
   1   0   0    0
   1  -1   0    0
   0   0   1   1/2
)
c 2x,x,z +1 { m010 | 0 0 1/2 }
22 -x, -x+y, z+1/2, +1
mx,mx-my,-mz
(
  -1   0   0    0
  -1   1   0    0
   0   0   1   1/2
)
c 0,y,z +1 { m210 | 0 0 1/2 }
23 x-y, -y, z+1/2, +1
-mx+my,my,-mz
(
   1  -1   0    0
   0  -1   0    0
   0   0   1   1/2
)
c x,0,z +1 { m120 | 0 0 1/2 }
24 y, x, z+1/2, +1
-my,-mx,-mz
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
c x,x,z +1 { m1-10 | 0 0 1/2 }
25 x, y, z+1/2, -1
-mx,-my,-mz
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)'
t (0,0,1/2) -1 { 1' | 0 0 1/2 }
26 x-y, x, z+1/2, -1
-mx+my,-mx,-mz
(
   1  -1   0    0
   1   0   0    0
   0   0   1   1/2
)'
6+ (0,0,1/2) 0,0,z -1 { 6'+001 | 0 0 1/2 }
27 -y, x-y, z+1/2, -1
my,-mx+my,-mz
(
   0  -1   0    0
   1  -1   0    0
   0   0   1   1/2
)'
3+ (0,0,1/2) 0,0,z -1 { 3'+001 | 0 0 1/2 }
28 -x, -y, z+1/2, -1
mx,my,-mz
(
  -1   0   0    0
   0  -1   0    0
   0   0   1   1/2
)'
2 (0,0,1/2) 0,0,z -1 { 2'001 | 0 0 1/2 }
29 -x+y, -x, z+1/2, -1
mx-my,mx,-mz
(
  -1   1   0    0
  -1   0   0    0
   0   0   1   1/2
)'
3- (0,0,1/2) 0,0,z -1 { 3'-001 | 0 0 1/2 }
30 y, -x+y, z+1/2, -1
-my,mx-my,-mz
(
   0   1   0    0
  -1   1   0    0
   0   0   1   1/2
)'
6- (0,0,1/2) 0,0,z -1 { 6'-001 | 0 0 1/2 }
31 x-y, -y, -z, -1
-mx+my,my,mz
(
   1  -1   0    0
   0  -1   0    0
   0   0  -1    0
)'
2 x,0,0 -1 { 2'100 | 0 }
32 y, x, -z, -1
-my,-mx,mz
(
   0   1   0    0
   1   0   0    0
   0   0  -1    0
)'
2 x,x,0 -1 { 2'110 | 0 }
33 -x, -x+y, -z, -1
mx,mx-my,mz
(
  -1   0   0    0
  -1   1   0    0
   0   0  -1    0
)'
2 0,y,0 -1 { 2'010 | 0 }
34 x, x-y, -z, -1
-mx,-mx+my,mz
(
   1   0   0    0
   1  -1   0    0
   0   0  -1    0
)'
2 2x,x,0 -1 { 2'210 | 0 }
35 -x+y, y, -z, -1
mx-my,-my,mz
(
  -1   1   0    0
   0   1   0    0
   0   0  -1    0
)'
2 x,2x,0 -1 { 2'120 | 0 }
36 -y, -x, -z, -1
my,mx,mz
(
   0  -1   0    0
  -1   0   0    0
   0   0  -1    0
)'
2 x,-x,0 -1 { 2'1-10 | 0 }
37 -x, -y, -z+1/2, -1
-mx,-my,-mz
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)'
-1 0,0,1/4 -1 { -1' | 0 0 1/2 }
38 -x+y, -x, -z+1/2, -1
-mx+my,-mx,-mz
(
  -1   1   0    0
  -1   0   0    0
   0   0  -1   1/2
)'
-6+ 0,0,z 0,0,1/4 -1 { -6'+001 | 0 0 1/2 }
39 y, -x+y, -z+1/2, -1
my,-mx+my,-mz
(
   0   1   0    0
  -1   1   0    0
   0   0  -1   1/2
)'
-3+ 0,0,z 0,0,1/4 -1 { -3'+001 | 0 0 1/2 }
40 x, y, -z+1/2, -1
mx,my,-mz
(
   1   0   0    0
   0   1   0    0
   0   0  -1   1/2
)'
m x,y,1/4 -1 { m'001 | 0 0 1/2 }
41 x-y, x, -z+1/2, -1
mx-my,mx,-mz
(
   1  -1   0    0
   1   0   0    0
   0   0  -1   1/2
)'
-3- 0,0,z 0,0,1/4 -1 { -3'-001 | 0 0 1/2 }
42 -y, x-y, -z+1/2, -1
-my,mx-my,-mz
(
   0  -1   0    0
   1  -1   0    0
   0   0  -1   1/2
)'
-6- 0,0,z 0,0,1/4 -1 { -6'-001 | 0 0 1/2 }
43 -x+y, y, z, -1
-mx+my,my,mz
(
  -1   1   0    0
   0   1   0    0
   0   0   1    0
)'
m x,2x,z -1 { m'100 | 0 }
44 -y, -x, z, -1
-my,-mx,mz
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)'
m x,-x,z -1 { m'110 | 0 }
45 x, x-y, z, -1
mx,mx-my,mz
(
   1   0   0    0
   1  -1   0    0
   0   0   1    0
)'
m 2x,x,z -1 { m'010 | 0 }
46 -x, -x+y, z, -1
-mx,-mx+my,mz
(
  -1   0   0    0
  -1   1   0    0
   0   0   1    0
)'
m 0,y,z -1 { m'210 | 0 }
47 x-y, -y, z, -1
mx-my,-my,mz
(
   1  -1   0    0
   0  -1   0    0
   0   0   1    0
)'
m x,0,z -1 { m'120 | 0 }
48 y, x, z, -1
my,mx,mz
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)'
m x,x,z -1 { m'1-10 | 0 }

Go to the list of the Wyckoff Positions of the Group Pc6/mcc (#192.252)
Go to the Systematic Absences for the Group Pc6/mcc (#192.252)

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