Cm No. 8 Cs3


C1m1 A1m1 I1m1

UNIQUE AXIS b

CELL CHOICE 1

CELL CHOICE 2

CELL CHOICE 3
Axes Coordinates Wyckoff positions Axes Coordinates Axes Coordinates
  2a 4b    
I Maximal translationengleiche subgroups
[2] P1 (1) (1/2)(a - b), 2x, x + y, z; 1a 2 × 1a P1 a, b, x, x + y, 2z P1 a, x + y, 2y, y + z
b, c (1/2)(-b + c) (1/2)(-a + b - c), c
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P1a1 (7) x, y + (1/4), z 2a 2 × 2a P1c1 x, y + (1/4), z P1n1 x, y + (1/4), z
[2] P1m1 (6) 1a; 1b 2 × 2c P1m1 P1m1
   Enlarged unit cell, non-isomorphic
[2] C1c1 (9) a, b, 2c x, y, (1/2)z; 4a 2 × 4a A1n1 2a + c, (1/2)x, y, -(1/2)x + z; I1a1 2a, b, (1/2)(x + z), y, z;
+(0, 0, (1/2)) b, c +((1/2), 0, 0) -a + c +((1/2), 0, 0)
[2] C1c1 (9) a - 2c, b, 2c x, y, x + (1/2)z; 4a 2 × 4a I1a1 2a, b, c (1/2)x, y, z; I1a1 2a, b, (1/2)(x - z), y, z;
+(0, 0, (1/2)) +((1/2), 0, 0) a + c +((1/2), 0, 0)
[conventional setting]I1a1 a, b, 2c x, y + (1/4), (1/2)z;
+(0, 0, (1/2))
   Enlarged unit cell, isomorphic
[3] C1m1 a, 3b, c x, (1/3)y, z; 2a; 4b 3 × 4b A1m1 a, 3b, c x, (1/3)y, z; I1m1 a, 3b, c x, (1/3)y, z;
±(0, (1/3), 0) ±(0, (1/3), 0) ±(0, (1/3), 0)
[p] C1m1 a, pb, c x, (1/p)y, z; 2a; ((p - 1)/2) × 4b p × 4b A1m1 a, pb, c x, (1/p)y, z; I1m1 a, pb, c x, (1/p)y, z;
+(0, (u/p), 0) +(0, (u/p), 0) +(0, (u/p), 0)
p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1
[2] C1m1 a, b, 2c x, y, (1/2)z; 2 × 2a 2 × 4b A1m1 2a, b, c (1/2)x, y, z; I1m1 2a, b, -a + c (1/2)(x + z), y, z;
+(0, 0, (1/2)) +((1/2), 0, 0) +((1/2), 0, 0)
[2] I1m1 a, b, 2c x, y, (1/2)z; 2 × 2a 2 × 4b I1m1 2a, b, c (1/2)x, y, z; I1m1 2a, b, a + c (1/2)(x - z), y, z;
+(0, 0, (1/2)) +((1/2), 0, 0) +((1/2), 0, 0)
[3] C1m1 3a, b, c (1/3)x, y, z; 3 × 2a 3 × 4b A1m1 a + c, x, y, (1/3)(-x + z); I1m1 a, b, 3c x, y, (1/3)z;
±((1/3), 0, 0) b, 3c ±(0, 0, (1/3)) ±(0, 0, (1/3))
[3] C1m1 3a, b, (1/3)(x + z), y, z; 3 × 2a 3 × 4b A1m1 a - c, x, y, (1/3)(x + z); I1m1 3a, b, (1/3)(x - 2z), y, z;
-a + c ±((1/3), 0, 0) b, 3c ±(0, 0, (1/3)) 2a+c ±((1/3), 0, 0)
[3] C1m1 3a, b, (1/3)(x - z), y, z; 3 × 2a 3 × 4b A1m1 a, b, 3c x, y, (1/3)z; I1m1 3a, b, c (1/3)x, y, z;
a + c ±((1/3), 0, 0) ±(0, 0, (1/3)) ±((1/3), 0, 0)
[3] C1m1 a, b, 3c x, y, (1/3)z; 3 × 2a 3 × 4b A1m1 3a, b, c (1/3)x, y, z; I1m1 3a, b, (1/3)(x + 2z), y, z;
±(0, 0, (1/3)) +((1/3), 0, 0) -2a + c ±((1/3), 0, 0)
[p] C1m1 a, b, pc x, y, (1/p)z; p × 2a p × 4b A1m1 pa, b, c (1/p)x, y, z; I1m1 pa, b, c (1/p)x, y, z;
+(0, 0, (u/p)) +((u/p), 0, 0) ±((u/p), 0, 0)
p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 p = prime; >2; u = 1, . . ., p - 1
[p] C1m1 pa, b, (1/p)(x - qz), y, z; p × 2a p × 4b A1m1 a + qc, x, y, (1/p)(-qx + z); I1m1 a + 2qc, x, y, (1/p)(-2qx + z);
qa + c +((u/p), 0, 0) b, pc +(0, 0, (u/p)) b, pc +(0, 0, (u/p))
p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1;
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)


A11m B11m I11m

UNIQUE AXIS c

CELL CHOICE 1

CELL CHOICE 2

CELL CHOICE 3
Axes Coordinates Wyckoff positions Axes Coordinates Axes Coordinates
  2a 4b    
I Maximal translationengleiche subgroups
[2] P1 (1) a, (1/2)(b - c), c x, 2y, y + z; 1a 2 × 1a P1 (1/2)(a - c), 2x, y, y + z P1 a, b, x + z, y + z, 2z
b, c (1/2)(-a - b + c)
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P11b (7) x, y, z + (1/4) 2a 2 × 2a P11a x, y, z + (1/4) P11n x, y, z + (1/4)
[2] P11m (6) 1a; 1b 2 × 2c P11m P11m
   Enlarged unit cell, non-isomorphic
[2] A11a (9) 2a, b, c (1/2)x, y, z; 4a 2 × 4a B11n a, x - (1/2)y, (1/2)y, z; I11b a - b, x, (1/2)(x + y), z;
+((1/2), 0, 0) a + 2b, c +(0, (1/2), 0) 2b, c +(0, (1/2), 0)
[2] A11a (9) 2a, (1/2)x + y, y, z; 4a 2 × 4a I11b a, 2b, c x, (1/2)y, z; I11b a + b, x, (1/2)(-z + y), z;
-2a + b, c +((1/2), 0, 0) +(0, (1/2), 0) 2b, c +(0, (1/2), 0)
[conventional setting]I11b a, 2b, c x, (1/2)y, z + (1/4);
+((1/2), 0, 0)
   Enlarged unit cell, isomorphic
[3] A11m a, b, 3c x, y, (1/3)z; 2a; 4b 3 × 4b B11m a, b, 3c x, y, (1/3)z; I11m a, b, 3c x, y, (1/3)z;
±(0, 0, (1/3)) ±(0, 0, (1/3)) ±(0, 0, (1/3))
[p] A11m a, b, pc x, y, (1/p)z; 2a; ((p - 1)/2) × 4b p × 4b B11m a, b, pc x, y, (1/p)z; I11m a, b, pc x, y, (1/p)z;
+(0, 0, (u/p)) +(0, 0, (u/p)) +(0, 0, (u/p))
p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1 p = prime > 2; u = 1, . . ., p - 1
[2] A11m 2a, b, c (1/2)x, y, z; 2 × 2a 2 × 4b B11m a, 2b, c x, (1/2)y, z; I11m a - b, x, (1/2)(x + y), z;
+((1/2), 0, 0) +(0, (1/2), 0) 2b, c +(0, (1/2), 0)
[2] I11m 2a, b, c (1/2)x, y, z; 2 × 2a 2 × 4b I11m a, 2b, c x, (1/2)y, z; I11m a + b, x, (1/2)(-x + y), z;
+((1/2), 0, 0) +(0, (1/2), 0) 2b, c +(0, (1/2), 0)
[3] A11m a, 3b, c x, (1/3)y, z; 3 × 2a 3 × 4b B11m 3a, (1/3)(x - y), y, z; I11m 3a, b, c (1/3)x, y, z;
±(0, (1/3), 0) a + b, c ±((1/3), 0, 0) ±((1/3), 0, 0)
[3] A11m a - b, x, (1/3)(x + y), z; 3 × 2a 3 × 4b B11m 3a, (1/3)(x + y), y, z; I11m a + 2b, x, (1/3)(-2x + y), z;
3b, c ±(0, (1/3), 0) -a + b, c ±((1/3), 0, 0) 3b, c ±(0, (1/3), 0)
[3] A11m a + b, x, (1/3)(-x + y), z; 3 × 2a 3 × 4b B11m 3a, b, c (1/3)x, y, z; I11m a, 3b, c x, (1/3)y, z;
3b, c ±(0, (1/3), 0) ±((1/3), 0, 0) ±(0, (1/3), 0)
[3] A11m 3a, b, c (1/3)x, y, z; 3 × 2a 3 × 4b B11m a, 3b, c x, (1/3)y, z; I11m a - 2b, x, (1/3)(2x + y), z;
±((1/3), 0, 0) +(0, (1/3), 0) 3b, c ±(0, (1/3), 0)
[p] A11m pa, b, c (1/p)x, y, z; p × 2a p × 4b B11m a, pb, c x, (1/p)y, z; I11m a, pb, c x, (1/p)y, z;
+((u/p), 0, 0) +(0, (u/p), 0) ±(0, (u/p), 0)
p = prime; u = 1, . . ., p - 1 p = prime; u = 1, . . ., p - 1 p = prime; >2; u = 1, . . ., p - 1
[p] A11m a + qb, x, (1/p)(-qx + y), z; p × 2a p × 4b B11m pa, (1/p)(x - qy), y, z; I11m pa, (1/p)(x - 2qy), y, z;
pb, c +(0, (u/p), 0) qa + b, c +((u/p), 0, 0) 2qa + b, c +((u/p), 0, 0)
p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1; p = prime > 2; u = 1, . . ., p - 1;
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)









































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