Cmme No. 67 C2/m2/m2/e D2h21


Axes Coordinates Wyckoff positions
4a 4b 4c 4d 4e 4f 4g 8h 8i 8j 8k 8l
8m 8n 16o
I Maximal translationengleiche subgroups
[2] C2me (39) 4a 4b 4a 4b 4c 4c 4c 2 × 4a 2 × 4b 8d 8d 8d
[conventional setting]Aem2 c, -b, a z, -y, x 8d 2 × 4c 2 × 8d
[2] Cm2e (39) x + (1/4), y, z 4a 4b 4c 4c 4a 4b 4c 8d 8d 2 × 4a 2 × 4b 8d
[conventional setting]Aem2 c, a, b z, x + (1/4), y 2 × 4c 8d 2 × 8d
[2] Cmm2 (35) x, y + (1/4), z 4c 4c 4e 4e 4d 4d 2a; 2b 8f 8f 8f 8f 2 × 4c
2 × 4e 2 × 4d 2 × 8f
[2] C222 (21) x + (1/4), y, z 2a; 2b 2c; 2d 4e 4f 4g 4h 4k 2 × 4e 2 × 4f 2 × 4g 2 × 4h 4i; 4j
8l 8l 2 × 8l
[2] P112/a (13) a, x + y, 2y, z 2e 2e 2a 2c 2d 2b 2f 4g 4g 4g 4g 2 × 2e
(1/2)(-a + b), c 4g 4g 2 × 4g
[2] C2/m11 (12) 4g 4h 2a; 2b 2c; 2d 4e 4f 4i 2 × 4g 2 × 4h 8j 8j 8j
[conventional setting]C12/m1 b, -a, c y, -x, z 2 × 4i 8j 2 × 8j
[2] C12/m1 (12) x + (1/4), y + (1/4), z 4g 4h 4e 4f 2a; 2b 2c; 2d 4i 8j 8j 2 × 4g 2 × 4h 8j
8j 2 × 4i 2 × 8j
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] Pmab (57) x + (1/4), y + (1/4), z 4c 4c 4d 4d 4a 4b 4d 8e 8e 8e 8e 2 × 4c
[conventional setting]Pbcm c, -b, a z, -y - (1/4), x + (1/4) 2 × 4d 8e 2 × 8e
[2] Pbma (57) 4c 4c 4a 4b 4d 4d 4d 8e 8e 8e 8e 2 × 4c
[conventional setting]Pbcm c, a, b z, x, y 8e 2 × 4d 2 × 8e
[2] Pbaa (54) x + (1/4), y + (1/4), z 4d 4e 4d 4e 4a 4b 4c 2 × 4d 2 × 4e 8f 8f 8f
[conventional setting]Pcca b, c, a y + (1/4), z, x + (1/4) 8f 8f 2 × 8f
[2] Pbab (54) 4d 4e 4a 4b 4d 4e 4c 8f 8f 2 × 4d 2 × 4e 8f
[conventional setting]Pcca a, -c, b x, -z, y 8f 8f 2 × 8f
[2] Pmma (51) x + (1/4), y + (1/4), z 4g 4h 4k 4k 2a; 2b 2c; 2d 2e; 2f 8l 8l 2 × 4g 2 × 4h 8l
2 × 4k 4i; 4j 2 × 8l
[2] Pmmb (51) 4g 4h 2a; 2b 2c; 2d 4k 4k 2e; 2f 2 × 4g 2 × 4h 8l 8l 8l
[conventional setting]Pmma b, -a, c y, -x, z 4i; 4j 2 × 4k 2 × 8l
[2] Pmaa (49) 2e; 2f 2g; 2h 2a; 2d 2b; 2c 4i 4j 4q 4m; 4p 4n; 4o 2 × 4i 2 × 4j 4k; 4l
[conventional setting]Pccm b, c, a y, z, x 2 × 4q 8r 2 × 8r
[2] Pbmb (49) x + (1/4), y + (1/4), z 2e; 2g 2f; 2h 4k 4l 2a; 2c 2b; 2d 4q 2 × 4k 2 × 4l 4m; 4o 4n; 4p 4i; 4j
[conventional setting]Pccm c, a, b z, x + (1/4), y + (1/4) 8r 2 × 4q 2 × 8r
   Enlarged unit cell, non-isomorphic
[2] Imma (74) a, b, 2c x, y, (1/2)z; 8f 8g 4a; 4b 8h 8i 4c; 4d 2 × 4e 2 × 8f 16j 16j 2 × 8g 16j
+(0, 0, (1/2)) 2 × 8h 2 × 8i 2 × 16j
[2] Imma (74) a, b, 2c x, y, (1/2)z + (1/4); 8g 8f 8h 4a; 4b 4c; 4d 8i 2 × 4e 16j 2 × 8f 2 × 8g 16j 16j
+(0, 0, (1/2)) 2 × 8h 2 × 8i 2 × 16j
[2] Ibca (73) a, b, 2c x, y, (1/2)z; 8d 8c 8a 8c 8d 8b 8e 16f 2 × 8c 2 × 8d 16f 16f
+(0, 0, (1/2)) 16f 16f 2 × 16f
[2] Ibca (73) a, b, 2c x, y, (1/2)z + (1/4); 8c 8d 8c 8a 8b 8d 8e 2 × 8c 16f 16f 2 × 8d 16f
+(0, 0, (1/2)) 16f 16f 2 × 16f
[2] Imcb (72) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a; 4b 8g 4c; 4d 8j 8f 8e 8j 8h; 8i 16k 2 × 8f 16k 2 × 8g
[conventional setting]Ibam b, 2c, a y, (1/2)z, x; +(0, (1/2), 0) 2 × 8j 16k 2 × 16k


Axes Coordinates Wyckoff positions
4a 4b 4c 4d 4e 4f 4g 8h
8i 8j 8k 8l 8m 8n 16o
[2] Imcb (72) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 8g 4a; 4b 8j 4c; 4d 8e 8f 8j 16k
[conventional setting]Ibam b, 2c, a y, (1/2)z + (1/4), x; +(0, (1/2), 0) 8h; 8i 16k 2 × 8f 2 × 8g 2 × 8j 16k 2 × 16k
[2] Icma (72) a, b, 2c x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2)) 4a; 4b 8f 8g 8e 4c; 4d 8j 8j 2 × 8g
[conventional setting]Ibam 2c, a, b (1/2)z, x + (1/4), y + (1/4); +((1/2), 0, 0) 16k 8h; 8i 16k 2 × 8f 16k 2 × 8j 2 × 16k
[2] Icma (72) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) 8f 4a; 4b 8e 8g 8j 4c; 4d 8j 16k
[conventional setting]Ibam 2c, a, b (1/2)z + (1/4), x + (1/4), y + (1/4); +((1/2), 0, 0) 2 × 8g 16k 8h; 8i 2 × 8f 16k 2 × 8j 2 × 16k
[2] Ccce (68) a, b, 2c 4a; 4b 8g 8e 8c 8f 8d 8h 2 × 8e
origin 1: x + (1/4), y, (1/2)z; +(0, 0, (1/2)) 16i 2 × 8f 16i 2 × 8g 16i 16i 2 × 16i
origin 2: x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2))
[2] Ccce (68) a, b, 2c 8g 4a; 4b 8c 8e 8d 8f 8h 16i
origin 1: x + (1/4), y, (1/2)z + (1/4); +(0, 0, (1/2)) 2 × 8e 16i 2 × 8f 2 × 8g 16i 16i 2 × 16i
origin 2: x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2))
[2] Cmce (64) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 8d 8e 4a; 4b 8f 8c 8e 8f 2 × 8d
16g 16g 2 × 8e 16g 2 × 8f 16g 2 × 16g
[2] Cmce (64) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 8e 8d 8f 4a; 4b 8e 8c 8f 16g
2 × 8d 2 × 8e 16g 16g 2 × 8f 16g 2 × 16g
[2] Ccme (64) a, b, 2c x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2)) 8d 8e 8c 8e 4a; 4b 8f 8f 16g
[conventional setting]Cmce b, -a, 2c y + (1/4), -x - (1/4), (1/2)z; +(0, 0, (1/2)) 2 × 8e 2 × 8d 16g 16g 16g 2 × 8f 2 × 16g
[2] Ccme (64) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) 8e 8d 8e 8c 8f 4a; 4b 8f 2 × 8e
[conventional setting]Cmce b, -a, 2c y + (1/4), -x - (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) 16g 16g 2 × 8d 16g 16g 2 × 8f 2 × 16g
   Enlarged unit cell, isomorphic
[3] Cmme 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 4a; 8h 4b; 8i 4c; 8h 4d; 8i 4e; 8n 4f; 8n 4g; 8n 3 × 8h
3 × 8i 8j; 16o 8k; 16o 8l; 16o 8m; 16o 3 × 8n 3 × 16o
[p] Cmme pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 4a; 4b; 4c; 4d; 4e; 4f; 4g; p × 8h
p = prime > 2; ((p - 1)/2) × 8h ((p - 1)/2) × 8i ((p - 1)/2) × 8h ((p - 1)/2) × 8i ((p - 1)/2) × 8n ((p - 1)/2) × 8n ((p - 1)/2) × 8n
u = 1, . . ., p - 1 p × 8i 8j; 8k; 8l; 8m; p × 8n p × 16o
((p - 1)/2) × 16o ((p - 1)/2) × 16o ((p - 1)/2) × 16o ((p - 1)/2) × 16o
[3] Cmme a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 4a; 8j 4b; 8k 4c; 8m 4d; 8m 4e; 8j 4f; 8k 4g; 8m 8h; 16o
8i; 16o 3 × 8j 3 × 8k 8l; 16o 3 × 8m 8n; 16o 3 × 16o
[p] Cmme a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 4a; 4b; 4c; 4d; 4e; 4f; 4g; 8h;
p = prime > 2; ((p - 1)/2) × 8j ((p - 1)/2) × 8k ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8j ((p - 1)/2) × 8k ((p - 1)/2) × 8m ((p - 1)/2) × 16o
u = 1, . . ., p - 1 8i; p × 8j p × 8k 8l; p × 8m 8n; p × 16o
((p - 1)/2) × 16o ((p - 1)/2) × 16o ((p - 1)/2) × 16o
[2] Cmme a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a; 4b 8l 4c; 4d 8m 4e; 4f 8n 2 × 4g 8h; 8i
16o 8j; 8k 16o 2 × 8l 2 × 8m 2 × 8n 2 × 16o
[2] Cmme a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 8l 4a; 4b 8m 4c; 4d 8n 4e; 4f 2 × 4g 16o
8h; 8i 16o 8j; 8k 2 × 8l 2 × 8m 2 × 8n 2 × 16o
[3] Cmme a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 4a; 8l 4b; 8l 4c; 8m 4d; 8m 4e; 8n 4f; 8n 3 × 4g 8h; 16o
8i; 16o 8j; 16o 8k; 16o 3 × 8l 3 × 8m 3 × 8n 3 × 16o
[p] Cmme a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 4a; 4b; 4c; 4d; 4e; 4f; p × 4g p × 8h
p = prime > 2; ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8n ((p - 1)/2) × 8n ((p - 1)/2) × 16o
u = 1, . . ., p - 1 p × 8i 8j; 8k; p × 8l p × 8m p × 8n p × 16o
((p - 1)/2) × 16o ((p - 1)/2) × 16o ((p - 1)/2) × 16o


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
Aemm C → A→ B a→ b → c → a a→ b → c → a x→ y → z → x
Bmem A→ C→ B a← b ← c ← a a← b ← c ← a x← y ← z ← x









































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