P21/c C2h5 2/m Monoclinic info
No. 14 P121/c1 Patterson symmetry P12/m1
UNIQUE AXIS b, CELL CHOICE 1

symmetry group diagram

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Symmetry operations

(1)  1   (2)  2(0, 1/2, 0)   0, y1/4(3)  -1   0, 0, 0(4)  c   x1/4z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -xy + 1/2-z + 1/2(3) -x-y-z(4) x-y + 1/2z + 1/2
h0l: l = 2n
0k0: k = 2n
00l: l = 2n
    Special: as above, plus
2 d  -1 
1/2, 0, 1/2 1/21/2, 0
hkl: k  +  l  =  2n
2 c  -1 
0, 0, 1/2 0, 1/2, 0
hkl: k  +  l  =  2n
2 b  -1 
1/2, 0, 0 1/21/21/2
hkl: k  +  l  =  2n
2 a  -1 
0, 0, 0 0, 1/21/2
hkl: k  +  l  =  2n

Symmetry of special projections

Along [001]   p2gm
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p2gg
a' = b   b' = cp   
Origin at x, 0, 0
Along [010]   p2
a' = 1/2c   b' = a   
Origin at 0, y, 0

UNIQUE AXIS b, DIFFERENT CELL CHOICES

symmetry group diagram

P121/c1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -xy + 1/2-z + 1/2(3) -x-y-z(4) x-y + 1/2z + 1/2
h0l: l = 2n
0k0: k = 2n
00l: l = 2n
    Special: as above, plus
2 d  -1 
1/2, 0, 1/2 1/21/2, 0
hkl: k  +  l  =  2n
2 c  -1 
0, 0, 1/2 0, 1/2, 0
hkl: k  +  l  =  2n
2 b  -1 
1/2, 0, 0 1/21/21/2
hkl: k  +  l  =  2n
2 a  -1 
0, 0, 0 0, 1/21/2
hkl: k  +  l  =  2n

P121/n1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x + 1/2y + 1/2-z + 1/2(3) -x-y-z(4) x + 1/2-y + 1/2z + 1/2
h0l: h + l = 2n
0k0: k = 2n
h00: h = 2n
00l: l = 2n
    Special: as above, plus
2 d  -1 
1/2, 0, 0 0, 1/21/2
hkl: h  +  k  +  l  =  2n
2 c  -1 
1/2, 0, 1/2 0, 1/2, 0
hkl: h  +  k  +  l  =  2n
2 b  -1 
0, 0, 1/2 1/21/2, 0
hkl: h  +  k  +  l  =  2n
2 a  -1 
0, 0, 0 1/21/21/2
hkl: h  +  k  +  l  =  2n

P121/a1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x + 1/2y + 1/2-z(3) -x-y-z(4) x + 1/2-y + 1/2z
h0l: h = 2n
0k0: k = 2n
h00: h = 2n
    Special: as above, plus
2 d  -1 
0, 0, 1/2 1/21/21/2
hkl: h  +  k  =  2n
2 c  -1 
1/2, 0, 0 0, 1/2, 0
hkl: h  +  k  =  2n
2 b  -1 
1/2, 0, 1/2 0, 1/21/2
hkl: h  +  k  =  2n
2 a  -1 
0, 0, 0 1/21/2, 0
hkl: h  +  k  =  2n





P21/c C2h5 2/m Monoclinic info
No. 14 P1121/a Patterson symmetry P112/m
UNIQUE AXIS c, CELL CHOICE 1

symmetry group diagram

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Symmetry operations

(1)  1   (2)  2(0, 0, 1/2)   1/4, 0, z(3)  -1   0, 0, 0(4)  a   xy1/4

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x + 1/2-yz + 1/2(3) -x-y-z(4) x + 1/2y-z + 1/2
hk0: h = 2n
00l: l = 2n
h00: h = 2n
    Special: as above, plus
2 d  -1 
1/21/2, 0 0, 1/21/2
hkl: h  +  l  =  2n
2 c  -1 
1/2, 0, 0 0, 0, 1/2
hkl: h  +  l  =  2n
2 b  -1 
0, 1/2, 0 1/21/21/2
hkl: h  +  l  =  2n
2 a  -1 
0, 0, 0 1/2, 0, 1/2
hkl: h  +  l  =  2n

Symmetry of special projections

Along [001]   p2
a' = 1/2a   b' = b   
Origin at 0, 0, z
Along [100]   p2gm
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p2gg
a' = c   b' = ap   
Origin at 0, y, 0

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

P1121/a

UNIQUE AXIS c, CELL CHOICE 1

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x + 1/2-yz + 1/2(3) -x-y-z(4) x + 1/2y-z + 1/2
hk0: h = 2n
00l: l = 2n
h00: h = 2n
    Special: as above, plus
2 d  -1 
1/21/2, 0 0, 1/21/2
hkl: h  +  l  =  2n
2 c  -1 
1/2, 0, 0 0, 0, 1/2
hkl: h  +  l  =  2n
2 b  -1 
0, 1/2, 0 1/21/21/2
hkl: h  +  l  =  2n
2 a  -1 
0, 0, 0 1/2, 0, 1/2
hkl: h  +  l  =  2n

P1121/n

UNIQUE AXIS c, CELL CHOICE 2

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x + 1/2-y + 1/2z + 1/2(3) -x-y-z(4) x + 1/2y + 1/2-z + 1/2
hk0: h + k = 2n
00l: l = 2n
h00: h = 2n
0k0: k = 2n
    Special: as above, plus
2 d  -1 
0, 1/2, 0 1/2, 0, 1/2
hkl: h  +  k  +  l  =  2n
2 c  -1 
1/21/2, 0 0, 0, 1/2
hkl: h  +  k  +  l  =  2n
2 b  -1 
1/2, 0, 0 0, 1/21/2
hkl: h  +  k  +  l  =  2n
2 a  -1 
0, 0, 0 1/21/21/2
hkl: h  +  k  +  l  =  2n

P1121/b

UNIQUE AXIS c, CELL CHOICE 3

cell choice

Origin at -1

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 e 1
(1) xyz(2) -x-y + 1/2z + 1/2(3) -x-y-z(4) xy + 1/2-z + 1/2
hk0: k = 2n
00l: l = 2n
0k0: k = 2n
    Special: as above, plus
2 d  -1 
1/2, 0, 0 1/21/21/2
hkl: k  +  l  =  2n
2 c  -1 
0, 1/2, 0 0, 0, 1/2
hkl: k  +  l  =  2n
2 b  -1 
1/21/2, 0 1/2, 0, 1/2
hkl: k  +  l  =  2n
2 a  -1 
0, 0, 0 0, 1/21/2
hkl: k  +  l  =  2n








































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