P4/nmm No. 129 P4/n21/m2/m D4h7


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 2c 4d 4e 4f 8g 8h 8i 8j 16k
I Maximal translationengleiche subgroups
[2] P-4m2 (115) x + (1/4), y - (1/4), z 1a; 1b 1c; 1d 2g 4h 4i 2e; 2f 2 × 4h 2 × 4i 4j; 4k 8l 2 × 8l
[2] P-421m (113) x + (1/4), y - (1/4), z 2a 2b 2c 4e 4e 4d 8f 8f 8f 2 × 4e 2 × 8f
[2] P4mm (99) x + (1/2), y, z x - (1/4), y - (1/4), z 2c 2c 1a; 1b 4d 4d 2 × 2c 8g 8g 4e; 4f 2 × 4d 2 × 8g
[2] P4212 (90) x + (1/4), y - (1/4), z 2a 2b 2c 4e 4f 4d 2 × 4e 2 × 4f 8g 8g 2 × 8g
[2] P4/n (85) 2a 2b 2c 4d 4e 4f 8g 8g 8g 8g 2 × 8g
[2] Pmmn (59) 2a(b*) 2a(b*) 2b(a*) 4c 4d 2 × 2a(b*) 8g 8g 4e; 4f 8g 2 × 8g
[2] Cmme a - b, (1/2)(x - y) + (1/4), (1/2)(x - y), 4a 4b 4g 4c; 4e 4d; 4f 8l 8h; 8j 8i; 8k 16o 8m; 8n 2 × 16o
  (67) a + b, c (1/2)(x + y), z (1/2)(x + y), z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/ncm a, b, 2c x, y, (1/2)z; x, y, (1/2)z + (1/4); 4b 4a 4e 8i 4c; 4d 8f 16j 8g; 8h 16j 2 × 8i 2 × 16j
  (138) +(0, 0, (1/2)) +(0, 0, (1/2))
[2] P42/ncm a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z; 4a 4b 4e 4c; 4d 8i 8f 8g; 8h 16j 16j 2 × 8i 2 × 16j
  (138) +(0, 0, (1/2)) +(0, 0, (1/2))
[2] P42/nmc a, b, 2c x, y, (1/2)z; x, y, (1/2)z + (1/4); 2a; 2b 4c 4d 8f 8e 2 × 4c 2 × 8f 16 h 2 × 8g 16h 2 × 16h
  (137) +(0, 0, (1/2)) +(0, 0, (1/2))
[2] P42/nmc a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z; 4c 2a; 2b 4d 8e 8f 2 × 4c 16h 2 × 8f 2 × 8g 16h 2 × 16h
  (137) +(0, 0, (1/2)) +(0, 0, (1/2))
[2] P4/ncc a, b, 2c x, y, (1/2)z; x, y, (1/2)z; 4b 4a 4c 8d 8f 8e 16g 2 × 8f 16g 16g 2 × 16g
  (130) +(0, 0, (1/2)) +(0, 0, (1/2))
[2] P4/ncc a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z + (1/4); 4a 4b 4c 8f 8d 8e 2 × 8f 16g 16g 16g 2 × 16g
  (130) +(0, 0, (1/2)) +(0, 0, (1/2))
   Enlarged unit cell, isomorphic
[2] P4/nmm a, b, 2c x, y, (1/2)z; x, y, (1/2)z; 2a; 2b 4f 2 × 2c 4d; 4e 8j 2 × 4f 8g; 8h 16k 2 × 8i 2 × 8j 2 × 16k
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] P4/nmm a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z + (1/4); 4f 2a; 2b 2 × 2c 8j 4d; 4e 2 × 4f 16k 8g; 8h 2 × 8i 2 × 8j 2 × 16k
+(0, 0, (1/2)) +(0, 0, (1/2))
[3] P4/nmm a, b, 3c x, y, (1/3)z; x, y, (1/3)z; 2a; 4f 2b; 4f 3 × 2c 4d; 8j 4e; 8j 3 × 4f 8g; 16k 8h; 16k 3 × 8i 3 × 8j 3 × 16k
±(0, 0, (1/3)) ±(0, 0, (1/3))


Wyckoff positions
2a 2b 2c 4d 4e
4f 8g 8h 8i
8j 16k
[p] P4/nmm a, b, pc x, y, (1/p)z; x, y, (1/p)z; 2a; ((p - 1)/2) × 4f 2b; ((p - 1)/2) × 4f p × 2c 4d; ((p - 1)/2) × 8j 4e; ((p - 1)/2) × 8j
+(0, 0, (u/p)) +(0, 0, (u/p)) p × 4f 8g; ((p - 1)/2) × 16k 8h; ((p - 1)/2) × 16k p × 8i
p = prime > 2; u = 1, . . . p - 1 p × 8j p × 16k
[9] P4/nmm 3a, 3b, c (1/3)x, (1/3)y, z; (1/3)x, (1/3)y, z; 2a; 8g; 8i 2b; 8h; 8i 2c; 8i; 8j 4d; 8g; 8j; 16k 4e; 8h; 8j; 16k
±((1/3), 0, 0); ±(0, (1/3), 0); 4f; 2 × 8i; 16k 3 × 8g; 3 × 16k 3 × 8h; × 16k 3 × 8i; 3 × 16k
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) 3 × 8j; 3 × 16k 9 × 16k
[p2] P4/nmm pa, pb, c (1/p)x, (1/p)y, z; (1/p)x, (1/p)y, z; 2a; ((p - 1)/2) × 8g; 2b; ((p - 1)/2) × 8h; 2c; ((p - 1)/2) × 8i; 4d; ((p - 1)/2) × 8g; 4e; ((p - 1)/2) × 8h;
+((u/p), (v/p), 0) +((u/p), (v/p), 0) ((p - 1)/2) × 8i; ((p - 1)/2) × 8i; ((p - 1)/2) × 8j; ((p - 1)/2) × 8j; ((p - 1)/2) × 8j;
p = prime > 2; (((p - 1)(p - 3))/8) × 16k (((p - 1)(p - 3))/8) × 16k (((p - 1)(p - 3))/8) × 16k (((p - 1)2)/4) × 16k (((p - 1)2)/4) × 16k
u, v = 1, . . . p - 1 4f; (p - 1) × 8i; p × 8g; p × 8h; p × 8i;
(((p - 1)2)/4) × 16k ((p(p - 1))/2) × 16k ((p(p - 1))/2) × 16k ((p(p - 1))/2) × 16k
p × 8j; p2 × 16k
((p(p - 1))/2) × 16k
* origin 2









































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