Fmmm No. 69 F2/m2/m2/m D2h23


Axes Coordinates Wyckoff positions
4a 4b 8c 8d 8e 8f 8g 8h 8i 16j 16k 16l 16m
16n 16o 32p
I Maximal translationengleiche subgroups
[2] F2mm (42) 4a 4a 8b 8c 8d 8b 2 × 4a 8d 8c 16e 16e 2 × 8b 16e
[conventional setting]Fmm2 b, c, a y, z, x 2 × 8c 2 × 8d 2 × 16e
[2] Fm2m (42) 4a 4a 8d 8b 8c 8b 8c 2 × 4a 8d 16e 2 × 8b 16e 2 × 8d
[conventional setting]Fmm2 c, a, b z, x, y 16e 2 × 8c 2 × 16e
[2] Fmm2 (42) 4a 4a 8c 8d 8b 8b 8d 8c 2 × 4a 2 × 8b 16e 16e 2 × 8c
2 × 8d 16e 2 × 16e
[2] F222 (22) 4a 4b 8j 8i 8h 4c; 4d 8e 8f 8g 2 × 8h 2 × 8i 2 × 8j 16k
16k 16k 2 × 16k
[2] B2/m11(12) a, (1/2)(b-c), c x, 2y, y + z 2a 2b 2c; 2d 4e 4f 4h 4g 4i 4i 8j 8j 2 × 4h 2 × 4i
[conventional setting]C12/m1 c, a, (1/2)(b-c) y + z, x, 2y 8j 8j 2 × 8j
[2] C12/m1(12) a, b, x + z, y, 2z 2a 2b 4f 2c; 2d 4e 4h 4i 4g 4i 8j 2 × 4h 8j 8j
(1/2)(-a + c) 2 × 4i 8j 2 × 8j
[2] A112/m(12) (1/2)(a - b), 2x, x + y, z 2a 2b 4e 4f 2c; 2d 4h 4i 4i 4g 2 × 4h 8j 8j 8j
b, c 8j 2 × 4i 2 × 8j
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] Aeaa (68) origin 1: x, y, z 4a 4b 8h 8d 8c 8h 8g 8e 8f 16i 16i 2 × 8h 16i
origin 2: x + (1/4), y, z + (1/4) 16i 16i 2 × 16i
[conventional setting]Ccce b, c, a y, z, x (origin 1)
origin 2: y, z + (1/4), x + (1/4)
[2] Bbeb (68) origin 1: x, y, z 4a 4b 8c 8h 8d 8h 8f 8g 8e 16i 2 × 8h 16i 16i
origin 2: x + (1/4), y + (1/4), z 16i 16i 2 × 16i
[conventional setting]Ccce c, a, b z, x, y (origin 1)
origin 2: z, x + (1/4), y + (1/4)
[2] Ccce (68) origin 1: x, y, z 4a 4b 8d 8c 8h 8h 8e 8f 8g 2 × 8h 16i 16i 16i
origin 2: x, y + (1/4), z + (1/4) 16i 16i 2 × 16i
[2] Aemm (67) x + (1/4), y, z + (1/4) 4g 4g 8l 4c; 4d 4e; 4f 4a; 4b 2 × 4g 8n 8m 8j; 8k 8h; 8i 2 × 8l 16o
[conventional setting]Cmme b, c, a y, z + (1/4), x + (1/4) 2 × 8m 2 × 8n 2 × 16o
[2] Bmem (67) x + (1/4), y + (1/4), z 4g 4g 4e; 4f 8l 4c; 4d 4a; 4b 8m 2 × 4g 8n 8h; 8i 2 × 8l 8j; 8k 2 × 8n
[conventional setting]Cmme c, a, b z, x + (1/4), y + (1/4) 16o 2 × 8m 2 × 16o
[2] Cmme (67) x, y + (1/4), z + (1/4) 4g 4g 4c; 4d 4e; 4f 8l 4a; 4b 8n 8m 2 × 4g 2 × 8l 8j; 8k 8h; 8i 2 × 8m
2 × 8n 16o 2 × 16o
[2] Amaa (66) x, y + (1/4), z + (1/4) 4e 4f 4c; 4d 8g 8h 4a; 4b 8k 8l 8l 2 × 8h 2 × 8g 8i; 8j 2 × 8l
[conventional setting]Cccm b, c, a y + (1/4), z + (1/4), x 16m 16m 2 × 16m
[2] Bbmb (66) x + (1/4), y, z + (1/4) 4e 4f 8h 4c; 4d 8g 4a; 4b 8l 8k 8l 2 × 8g 8i; 8j 2 × 8h 16m
[conventional setting]Cccm c, a, b z + (1/4), x + (1/4), y 2 × 8l 16m 2 × 16m
[2] Cccm (66) x + (1/4), y + (1/4), z 4e 4f 8g 8h 4c; 4d 4a; 4b 8l 8l 8k 8i; 8j 2 × 8h 2 × 8g 16m
16m 2 × 8l 2 × 16m
[2] Ammm (65) 2a; 2c 2b; 2d 4e; 4f 8n 8o 8m 4k; 4l 4g; 4h 4i; 4j 16r 16r 2 × 8m 8p; 8q
[conventional setting]Cmmm b, c, a y, z, x 2 × 8n 2 × 8o 2 × 16r
[2] Bmmm (65) 2a; 2c 2b; 2d 8o 4e; 4f 8n 8m 4i; 4j 4k; 4l 4g; 4h 16r 2 × 8m 16r 2 × 8o
[conventional setting]Cmmm c, a, b z, x, y 8p; 8q 2 × 8n 2 × 16r
[2] Cmmm (65) 2a; 2c 2b; 2d 8n 8o 4e; 4f 8m 4g; 4h 4i; 4j 4k; 4l 2 × 8m 16r 16r 2 × 8n
2 × 8o 8p; 8q 2 × 16r


Axes Coordinates Wyckoff positions
4a 4b 8c 8d 8e 8f 8g 8h 8i 16j
16k 16l 16m 16n 16o 32p
[2] Aema (64) 4a 4b 8c 8f 8e 8e 8f 8d 8f 2 × 8e
[conventional setting]Cmce b, c, a y, z, x 16g 16g 16g 2 × 8f 16g 2 × 16g
[2] Aeam (64) 4a 4b 8c 8e 8f 8e 8f 8f 8d 16g
[conventional setting]Cmce c, -b, a z, -y, x 2 × 8e 16g 16g 16g 2 × 8f 2 × 16g
[2] Bbem (64) 4a 4b 8e 8c 8f 8e 8f 8f 8d 16g
[conventional setting]Cmce c, a, b z, x, y 16g 2 × 8e 16g 16g 2 × 8f 2 × 16g
[2] Bmeb (64) 4a 4b 8f 8c 8e 8e 8d 8f 8f 2 × 8e
[conventional setting]Cmce a, -c, b x, -z, y 16g 16g 2 × 8f 16g 16g 2 × 16g
[2] Cmce (64) 4a 4b 8f 8e 8c 8e 8d 8f 8f 16g
2 × 8e 16g 2 × 8f 16g 16g 2 × 16g
[2] Ccme (64) 4a 4b 8e 8f 8c 8e 8f 8d 8f 16g
[conventional setting]Cmce b, -a, c y, -x, z 16g 2 × 8e 16g 2 × 8f 16g 2 × 16g
[2] Amam (63) x + (1/4), y + (1/4), z 4c 4c 8g 8d 4a; 4b 8e 8f 2 × 4c 8g 2 × 8e
[conventional setting]Cmcm c, -b, a z, -y - (1/4), x + (1/4) 16h 16h 2 × 8g 16h 2 × 8f 2 × 16h
[2] Amma (63) x + (1/4), y, z + (1/4) 4c 4c 8g 4a; 4b 8d 8e 8f 8g 2 × 4c 16h
[conventional setting]Cmcm b, c, a y, z + (1/4), x + (1/4) 2 × 8e 16h 2 × 8g 2 × 8f 16h 2 × 16h
[2] Bbmm (63) x + (1/4), y + (1/4), z 4c 4c 8d 8g 4a; 4b 8e 2 × 4c 8f 8g 2 × 8e
[conventional setting]Cmcm c, a, b z, x + (1/4), y + (1/4) 16h 16h 16h 2 × 8g 2 × 8f 2 × 16h
[2] Bmmb (63) x, y + (1/4), z + (1/4) 4c 4c 4a; 4b 8g 8d 8e 8g 8f 2 × 4c 16h
[conventional setting]Cmcm a, -c, b x, -z - (1/4), y + (1/4) 16h 2 × 8e 2 × 8f 2 × 8g 16h 2 × 16h
[2] Ccmm (63) x + (1/4), y, z + (1/4) 4c 4c 8d 4a; 4b 8g 8e 2 × 4c 8g 8f 16h
[conventional setting]Cmcm b, -a, c y, -x - (1/4), z + (1/4) 2 × 8e 16h 16h 2 × 8f 2 × 8g 2 × 16h
[2] Cmcm (63) x, y + (1/4), z + (1/4) 4c 4c 4a; 4b 8d 8g 8e 8g 2 × 4c 8f 16h
16h 2 × 8e 2 × 8f 16h 2 × 8g 2 × 16h
   Enlarged unit cell, isomorphic
[3] Fmmm 3a, b, c (1/3)x, y, z; 4a; 8g 4b; 8g 8c; 16l 8d; 16n 8e; 16o 8f; 16l 3 × 8g 8h; 16o 8i; 16n 16j; 32p
±((1/3), 0, 0) 16k; 32p 3 × 16l 16m; 32p 3 × 16n 3 × 16o 3 × 32p
[p] Fmmm pa, b, c (1/p)x, y, z; 4a; 4b; 8c; 8d; 8e; 8f; p × 8g 8h; 8i; 16j;
+((u/p), 0, 0) ((p - 1)/2) × 8g ((p - 1)/2) × 8g ((p - 1)/2) × 16l ((p - 1)/2) × 16n ((p - 1)/2) × 16o ((p - 1)/2) × 16l ((p - 1)/2) × 16o ((p - 1)/2) × 16n ((p - 1)/2) × 32p
p = prime > 2; 16k; p × 16l 16m; p × 16n p × 16o p × 32p
u = 1, . . ., p - 1 ((p - 1)/2) × 32p ((p - 1)/2) × 32p
[3] Fmmm a, 3b, c x, (1/3)y, z; 4a; 8h 4b; 8h 8c; 16m 8d; 16k 8e; 16o 8f; 16k 8g; 16o 3 × 8h 8i; 16m 16j; 32p
±(0, (1/3), 0) 3 × 16k 16l; 32p 3 × 16m 16n; 32p 3 × 16o 3 × 32p
[p] Fmmm a, pb, c x, (1/p)y, z; 4a; 4b; 8c; 8d; 8e; 8f; 8g; p × 8h 8i; 16j;
+(0, (u/p), 0) ((p - 1)/2) × 8h ((p - 1)/2) × 8h ((p - 1)/2) × 16m ((p - 1)/2) × 16k ((p - 1)/2) × 16o ((p - 1)/2) × 16k ((p - 1)/2) × 16o ((p - 1)/2) × 16m ((p - 1)/2) × 32p
p = prime > 2; p × 16k 16l; p × 16m 16n; p × 16o p × 32p
u = 1, . . ., p - 1 ((p - 1)/2) × 32p ((p - 1)/2) × 32p
[3] Fmmm a, b, 3c x, y, (1/3)z; 4a; 8i 4b; 8i 8c; 16m 8d; 16n 8e; 16j 8f; 16j 8g; 16n 8h; 16m 3 × 8i 3 × 16j
±(0, 0, (1/3)) 16 k; 32p 16l; 32p 3 × 16m 3 × 16n 16o; 32p 3 × 32p
[p] Fmmm a, b, pc x, y, (1/p)z; 4a; 4b; 8c; 8d; 8e; 8f; 8g; 8h; p × 8i p × 16j
+(0, 0, (u/p)) ((p - 1)/2) × 8i ((p - 1)/2) × 8i ((p - 1)/2) × 16m ((p - 1)/2) × 16n ((p - 1)/2) × 16j ((p - 1)/2) × 16j ((p - 1)/2) × 16n ((p - 1)/2) × 16m
p = prime > 2; 16k; 16l; p × 16m p × 16n 16o; p × 32p
u = 1, . . ., p - 1 ((p - 1)/2) × 32p ((p - 1)/2) × 32p ((p - 1)/2) × 32p









































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