Cmmm No. 65 C2/m2/m2/m D2h19


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 4i 4j 4k 4l
8m 8n 8o 8p 8q 16r
I Maximal translationengleiche subgroups
[2] C2mm (38) 2a 2a 2b 2b 4d 4e 2 × 2a 2 × 2b 4d 4e 4c 4c
[conventional setting]Amm2 c, -b, a z, -y, x 8f 8f 2 × 4c 2 × 4d 2 × 4e 2 × 8f
[2] Cm2m (38) 2a 2a 2b 2b 4d 4e 4d 4e 2 × 2a 2 × 2b 4c 4c
[conventional setting]Amm2 c, a, b z, x, y 8f 2 × 4c 8f 2 × 4d 2 × 4e 2 × 8f
[2] Cmm2 (35) 2a 2b 2b 2a 4c 4c 4d 4d 4e 4e 2 × 2a 2 × 2b
2 × 4c 2 × 4e 2 × 4d 8f 8f 2 × 8f
[2] C222 (21) 2a 2b 2c 2d 4k 4k 4e 4f 4g 4h 4i 4j
2 × 4k 8l 8l 8l 8l 2 × 8l
[2] C2/m11(12) 2a 2b 2d 2c 4e 4f 4g 4h 4i 4i 4i 4i
[conventional setting]C12/m1 b, -a, c y, -x, z 8j 2 × 4i 8j 8j 8j 2 × 8j
[2] C12/m1(12) 2a 2b 2d 2c 4e 4f 4i 4i 4g 4h 4i 4i
8j 8j 2 × 4i 8j 8j 2 × 8j
[2] P112/m(10) a, (1/2)(-a + b), c x + y, 2y, z 1a 1c 1f 1b 1d; 1g 1e; 1h 2m 2n 2m 2n 2i 2k
2j; 2l 4o 4o 2 × 2m 2 × 2n 2 × 4o
  or: (1/2)(a - b), x - y, x + y, z 1a 1g 1h 1b 1c; 1d 1e; 1f 2m 2n 2m 2n 2i 2l
(1/2)(a + b), c 2j; 2k 4o 4o 2 × 2m 2 × 2n 2 × 4o
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] Pmmn (59) origin 1: x, y, z 2a 2b 2b 2a 4c 4d 4f 4f 4e 4e 2 × 2a 2 × 2b
origin 2: x + (1/4), y + (1/4), z 8g 2 × 4e 2 × 4f 8g 8g 2 × 8g
[2] Pbam (55) 2a 2c 2d 2b 4g 4h 4g 4h 4g 4h 4e 4f
8i 8i 8i 2 × 4g 2 × 4h 2 × 8i
[2] Pbmn (53) 2a 2b 2c 2d 4g 4g 4h 4h 4e 4f 4h 4h
[conventional setting]Pmna b, c, a y, z, x 2 × 4g 8i 2 × 4h 8i 8i 2 × 8i
[2] Pman (53) 2a 2b 2c 2d 4g 4g 4e 4f 4h 4h 4h 4h
[conventional setting]Pmna a, -c, b x, -z, y 2 × 4g 2 × 4h 8i 8i 8i 2 × 8i
[2] Pbmm (51) x + (1/4), y + (1/4), z 2e 2e 2f 2f 2a; 2c 2b; 2d 2 × 2e 2 × 2f 4i 4j 4k 4k
[conventional setting]Pmma b, c, a y + (1/4), z, x + (1/4) 4g; 4h 8l 2 × 4k 2 × 4i 2 × 4j 2 × 8l
[2] Pmam (51) x + (1/4), y + (1/4), z 2e 2e 2f 2f 2a; 2c 2b; 2d 4i 4j 2 × 2e 2 × 2f 4k 4k
[conventional setting]Pmma a, -c, b x + (1/4), -z, y + (1/4) 4g; 4h 2 × 4k 8l 2 × 4i 2 × 4j 2 × 8l
[2] Pban (50) origin 1: x, y, z 2a 2b 2c 2d 4e 4f 4g 4h 4i 4j 4k 4l
origin 2: x + (1/4), y + (1/4), z 8m 8m 8m 8m 8m 2 × 8m
[2] Pmmm (47) 1a; 1f 1b; 1e 1d; 1g 1c; 1h 4y 4z 2i; 2k 2j; 2l 2m; 2o 2n; 2p 2q; 2t 2r; 2s
8[alpha] 4u; 4v 4w; 4x 2 × 4y 2 × 4z 2 × 8[alpha]


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 4i 4j 4k 4l
8m 8n 8o 8p 8q 16r
   Enlarged unit cell, non-isomorphic
[2] Ibmm (74) a, b, 2c x, y, (1/2)z; 4a 4b 4e 4e 8g 4c; 4d 8h 2 × 4e 8f 8i 8h 8h
+(0, 0, (1/2)) 2 × 8g 16j 2 × 8h 16j 2 × 8i 2 × 16j
[conventional setting]Imma b, 2c, a y, (1/2)z, x;
+(0, (1/2), 0)
[2] Ibmm (74) a, b, 2c x, y, (1/2)z + (1/4); 4e 4e 4b 4a 4c; 4d 8g 2 × 4e 8h 8i 8f 8h 8h
+(0, 0, (1/2)) 2 × 8g 16j 2 × 8h 2 × 8i 16j 2 × 16j
[conventional setting]Imma b, 2c, a y, (1/2)z + (1/4), x;
+(0, (1/2), 0)
[2] Imam (74) a, b, 2c x, y, (1/2)z; 4a 4b 4e 4e 8g 4c; 4d 8f 8i 8h 2 × 4e 8h 8h
+(0, 0, (1/2)) 2 × 8g 2 × 8h 16j 16j 2 × 8i 2 × 16j
[conventional setting]Imma a, -2c, b x, -(1/2)z, y;
+(0, (1/2), 0)
[2] Imam (74) a, b, 2c x, y, (1/2)z + (1/4); 4e 4e 4b 4a 4c; 4d 8g 8i 8f 2 × 4e 8h 8h 8h
+(0, 0, (1/2)) 2 × 8g 2 × 8h 16j 2 × 8i 16j 2 × 16j
[conventional setting]Imma a, -2c, b x, -(1/2)z - (1/4), y;
+(0, 0, (1/2))
[2] Ibam (72) a, b, 2c x, y, (1/2)z; 4c 4d 4b 4a 8j 8e 8j 8f 8j 8g 8h 8i
+(0, 0, (1/2)) 16k 16k 16k 2 × 8j 16k 2 × 16k
[2] Ibam (72) a, b, 2c x, y, (1/2)z + (1/4); 4a 4b 4d 4c 8e 8j 8f 8j 8g 8j 8h 8i
+(0, 0, (1/2)) 16k 16k 16k 16k 2 × 8j 2 × 16k
[2] Immm(71) a, b, 2c x, y, (1/2)z; 2a; 2c 2b; 2d 4j 4i 8n 8k 4e; 4f 8m 4g; 4h 8l 2 × 4i 2 × 4j
+(0, 0, (1/2)) 16o 2 × 8l 2 × 8m 2 × 8n 16o 2 × 16o
[2] Immm(71) a, b, 2c x, y, (1/2)z + (1/4); 4i 4j 2b; 2d 2a; 2c 8k 8n 8m 4e; 4f 8l 4g; 4h 2 × 4i 2 × 4j
+(0, 0, (1/2)) 16o 2 × 8l 2 × 8m 16o 2 × 8n 2 × 16o
[2] Cccm (66) a, b, 2c x, y, (1/2)z; 4c 4d 4b 4a 4e; 4f 8k 8l 8g 8l 8h 8i 8j
+(0, 0, (1/2)) 2 × 8k 16m 16m 2 × 8l 16m 2 × 16m
[2] Cccm (66) a, b, 2c x, y, (1/2)z + (1/4); 4a 4b 4d 4c 8k 4e; 4f 8g 8l 8h 8l 8i 8j
+(0, 0, (1/2)) 2 × 8k 16m 16m 16m 2 × 8l 2 × 16m
[2] Ccmm (63) a, b, 2c x, y, (1/2)z; 4a 4b 4c 4c 8d 8g 8f 2 × 4c 8e 8g 8f 8f
+(0, 0, (1/2)) 16h 16h 2 × 8f 16h 2 × 8g 2 × 16h
[conventional setting]Cmcm b, -a, 2c y, -x, (1/2)z;
+(0, 0, (1/2))
[2] Ccmm (63) a, b, 2c x, y, (1/2)z + (1/4); 4c 4c 4b 4a 8g 8d 2 × 4c 8f 8g 8e 8f 8f
+(0, 0, (1/2)) 16h 16h 2 × 8f 2 × 8g 16h 2 × 16h
[conventional setting]Cmcm b, -a, 2c y, -x, (1/2)z + (1/4);
+(0, 0, (1/2))
[2] Cmcm (63) a, b, 2c x, y, (1/2)z; 4a 4b 4c 4c 8d 8g 8e 8g 8f 2 × 4c 8f 8f
+(0, 0, (1/2)) 16h 2 × 8f 16h 16h 2 × 8g 2 × 16h
[2] Cmcm (63) a, b, 2c x, y, (1/2)z + (1/4); 4c 4c 4b 4a 8g 8d 8g 8e 2 × 4c 8f 8f 8f
+(0, 0, (1/2)) 16h 2 × 8f 16h 2 × 8g 16h 2 × 16h


Axes Coordinates Wyckoff positions
  2a 2b 2c 2d 4e 4f 4g 4h 4i 4j
4k 4l 8m 8n 8o 8p 8q 16r
   Enlarged unit cell, isomorphic
[3] Cmmm 3a, b, c (1/3)x, y, z; 2a; 4g 2b; 4g 2c; 4h 2d; 4h 4e; 8p 4f; 8q 3 × 4g 3 × 4h 4i; 8p 4j; 8q
±((1/3), 0, 0) 4k; 8o 4l; 8o 8m; 16r 8n; 16r 3 × 8o 3 × 8p 3 × 8q 3 × 16r
[p] Cmmm pa, b, c (1/p)x, y, z; 2a; 2b; 2c; 2d; 4e; 4f; p × 4g p × 4h 4i; 4j;
+((u/p), 0, 0) ((p - 1)/2) × 4g ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 8p ((p - 1)/2) × 8q ((p - 1)/2) × 8p ((p - 1)/2) × 8q
p = prime > 2; 4k; 4l; 8m; 8n; p × 8o p × 8p p × 8q p × 16r
u = 1, . . ., p - 1 ((p - 1)/2) × 8o ((p - 1)/2) × 8o ((p - 1)/2) × 16r ((p - 1)/2) × 16r
[3] Cmmm a, 3b, c x, (1/3)y, z; 2a; 4i 2b; 4i 2c; 4j 2d; 4j 4e; 8p 4f; 8q 4g; 8p 4h; 8q 3 × 4i 3 × 4j
±(0, (1/3), 0) 4k; 8n 4l; 8n 8m; 16r 3 × 8n 8o; 16r 3 × 8p 3 × 8q 3 × 16r
[p] Cmmm a, pb, c x, (1/p)y, z; 2a; 2b; 2c; 2d; 4e; 4f; 4g; 4h; p × 4i p × 4j
+(0, (u/p), 0) ((p - 1)/2) × 4i ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/2) × 8p ((p - 1)/2) × 8q ((p - 1)/2) × 8p ((p - 1)/2) × 8q
p = prime > 2; 4k; 4l; 8m; p × 8n 8o; p × 8p p × 8q p × 16r
u = 1, . . ., p - 1 ((p - 1)/2) × 8n ((p - 1)/2) × 8n ((p - 1)/2) × 16r ((p - 1)/2) × 16r
[2] Cmmm a, b, 2c x, y, (1/2)z; 2a; 2d 2b; 2c 4l 4k 4e; 4f 8m 4g; 4h 8o 4i; 4j 8n
+(0, 0, (1/2)) 2 × 4k 2 × 4l 2 × 8m 2 × 8n 2 × 8o 8p; 8q 16r 2 × 16r
[2] Cmmm a, b, 2c x, y, (1/2)z + (1/4); 4k 4l 2b; 2c 2a; 2d 8m 4e; 4f 8o 4g; 4h 8n 4i; 4j
+(0, 0, (1/2)) 2 × 4k 2 × 4l 2 × 8m 2 × 8n 2 × 8o 16r 8p; 8q 2 × 16r
[3] Cmmm a, b, 3c x, y, (1/3)z; 2a; 4k 2b; 4l 2c; 4l 2d; 4k 4e; 8m 4f; 8m 4g; 8o 4h; 8o 4i; 8n 4j; 8n
±(0, 0, (1/3)) 3 × 4k 3 × 4l 3 × 8m 3 × 8n 3 × 8o 8p; 16r 8q; 16r 3 × 16r
[p] Cmmm a, b, pc x, y, (1/p)z; 2a; 2b; 2c; 2d; 4e; 4f; 4g; 4h; 4i; 4j;
+(0, 0, (u/p)) ((p - 1)/2) × 4k ((p - 1)/2) × 4l ((p - 1)/2) × 4l ((p - 1)/2) × 4k ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8o ((p - 1)/2) × 8o ((p - 1)/2) × 8n ((p - 1)/2) × 8n
p = prime > 2; p × 4k p × 4l p × 8m p × 8n p × 8o 8p; 8q; p × 16r
u = 1, . . ., p - 1 ((p - 1)/2) × 16r ((p - 1)/2) × 16r


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









































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