P-1 Ci1 -1 Triclinic No. 2 P-1 Patterson symmetry P-1

Origin at -1

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1

Symmetry operations

 (1)  1 (2)  -1   0, 0, 0

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 i 1
 (1) x, y, z (2) -x, -y, -z
no conditions
Special: as above, plus
 1 h -1
 1/2, 1/2, 1/2
no extra conditions
 1 g -1
 0, 1/2, 1/2
no extra conditions
 1 f -1
 1/2, 0, 1/2
no extra conditions
 1 e -1
 1/2, 1/2, 0
no extra conditions
 1 d -1
 1/2, 0, 0
no extra conditions
 1 c -1
 0, 1/2, 0
no extra conditions
 1 b -1
 0, 0, 1/2
no extra conditions
 1 a -1
 0, 0, 0
no extra conditions

Symmetry of special projections

 Along [001]   p2a' = ap   b' = bp   Origin at 0, 0, z Along [100]   p2a' = bp   b' = cp   Origin at x, 0, 0 Along [010]   p2a' = cp   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [2] P-1 (a' = 2a or b' = 2b or c' = 2c or b' = b + c, c' = -b + c or a' = a - c, c' = a + c or a' = a + b, b' = -a + b or a' = b + c, b' = a + c, c' = a + b) (2)

Minimal non-isomorphic supergroups

 I [2] P2/m (10); [2] P21/m (11); [2] C2/m (12); [2] P2/c (13); [2] P21/c (14); [2] C2/c (15); [3] P-3 (147); [3] R-3 (148)
 II none