P42/nnm No. 134 P42/n2/n2/m D4h12


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 4c 4d 4e 4f 4g 8h
8i 8j 8k 8l 8m 16n
I Maximal translationengleiche subgroups
[2] P-4n2 x + (1/4), y - (1/4), z + (1/4) 2a 2b 4h 2c; 2d 4f 4g 4e 2 × 4h
(118) 8i 8i 2 × 4g 2 × 4f 8i 2 × 8i
[2] P-42m x + (1/4), y - (1/4), z + (1/4) 1a; 1b 1c; 1d 2e; 2f 4m 4n 4n 2g; 2h 2 × 4m
(111) 4i; 4j 4k; 4l 8o 8o 2 × 4n 2 × 8o
[2] P42nm x + (1/4), y - (1/4), z 2a 2a 4b 4b 4c 4c 2 × 2a 2 × 4b
(102) 8d 8d 8d 8d 2 × 4c 2 × 8d
[2] P4222 x, y + (1/2), z x + (1/4), y + (1/4), z + (1/4) 2c 2d 2a; 2b 2e; 2f 4o 4n 4i 4g; 4h
(93) 4l; 4m 4j; 4k 2 × 4n 2 × 4o 8p 2 × 8p
[2] P42/n x, y + (1/2), z 2a 2b 4e 4e 4c 4d 4f 2 × 4e
(86) 8g 8g 8g 8g 8g 2 × 8g
[2] Pnnn 2a(d*) 2c(b*) 2b(a*); 2d(c*) 4l(k*) 4e 4f 4k(l*) 2 × 4l(k*)
(48) 4g(h*); 4i 4h(g*); 4j 8m 8m 8m 2 × 8m
[2] Cmme a + b, (1/2)(x + y), (1/2)(x + y), 4g 4g 8l 4a; 4b 4d; 4e 4c; 4f 2 × 4g 2 × 8l
(67) -a + b, c (1/2)(-x + y) + (1/4), z - (1/4) (1/2)(-x + y), z 16o 16o 8h; 8k 8i; 8j 8m; 8n 2 × 16o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] I41/acd a + b, (1/2)(x + y), (1/2)(x + y), 8a 8b 16f 16e 16e 16c 16d 32g
(142) -a + b, 2c (1/2)(-x + y), (1/2)z; (1/2)(-x + y), (1/2)z; 32g 2 × 16f 32g 2 × 16e 32g 2 × 32g
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/acd a + b, (1/2)(x + y), (1/2)(x + y), 8b 8a 16f 16e 16c 16e 16d 32g
(142) -a + b, 2c (1/2)(-x + y), (1/2)z + (1/4); (1/2)(-x + y), (1/2)z + (1/4); 2 × 16f 32 g 2 × 16e 32g 32g 2 × 32g
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/acd a + b, (1/2)(x + y) + (1/2), (1/2)(x + y) + (1/2), 8b 8a 16f 16e 16e 16c 16d 32g
(142) -a + b, 2c (1/2)(-x + y), (1/2)z; (1/2)(-x + y), (1/2)z; 2 × 16f 32g 32g 2 × 16e 32g 2 × 32g
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/acd a + b, (1/2)(x + y) + (1/2), (1/2)(x + y) + (1/2), 8a 8b 16f 16e 16c 16e 16d 32g
(142) -a + b, 2c (1/2)(-x + y), (1/2)z + (1/4); (1/2)(-x + y), (1/2)z + (1/4); 32g 2 × 16f 2 × 16e 32g 32g 2 × 32g
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/amd a + b, (1/2)(x + y), (1/2)(x + y), 4a; 4b 8e 16g 16f 16h 8c; 8d 2 × 8e 32i
(141) -a + b, 2c (1/2)(-x + y), (1/2)z; (1/2)(-x + y), (1/2)z; 2 × 16g 32 i 2 × 16f 32i 2 × 16h 2 × 32i
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/amd a + b, (1/2)(x + y), (1/2)(x + y), 8e 4a; 4b 16g 16f 8c; 8d 16h 2 × 8e 32i
(141) -a + b, 2c (1/2)(-x + y), (1/2)z + (1/4); (1/2)(-x + y), (1/2)z + (1/4); 32 i 2 × 16g 32i 2 × 16f 2 × 16h 2 × 32i
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/amd a + b, (1/2)(x + y) + (1/2), (1/2)(x + y) + (1/2), 8e 4a; 4b 16g 16f 16h 8c; 8d 2 × 8e 32i
(141) -a + b, 2c (1/2)(-x + y), (1/2)z; (1/2)(-x + y), (1/2)z; 32i 2 × 16g 2 × 16f 32i 2 × 16h 2 × 32i
+(0, 0, (1/2)) +(0, 0, (1/2))
[2] I41/amd a + b, (1/2)(x + y) + (1/2), (1/2)(x + y) + (1/2), 4a; 4b 8e 16g 16f 8c; 8d 16h 2 × 8e 32i
(141) -a + b, 2c (1/2)(-x + y), (1/2)z + (1/4); (1/2)(-x + y), (1/2)z + (1/4); 2 × 16g 32 i 32i 2 × 16f 2 × 16h 2 × 32i
+(0, 0, (1/2)) +(0, 0, (1/2))
* origin 2


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 4c 4d 4e
4f 4g 8h 8i 8j
8k 8l 8m 16n
   Enlarged unit cell, isomorphic
[3] P42/nnm a, b, 3c x, y, (1/3)z; x, y, (1/3)z; 2a(b*); 4g 2b(a*); 4g 4c; 8h 4d; 8h 4f(e*); 8m
±(0, 0, (1/3)) ±(0, 0, (1/3)) 4e(f*); 8m 3 × 4g 3 × 8h 8i(j*); 16n 8j(i*); 16n
8l(k*); 16n 8k(l*); 16n 3 × 8m 3 × 16n
[p] P42/nnm a, b, pc x, y, (1/p)z; x, y, (1/p)z; 2a(b† ); ((p - 1)/2) × 4g 2b(a† ); ((p - 1)/2) × 4g 4c; ((p - 1)/2) × 8h 4d; ((p - 1)/2) × 8h 4e(f‡ ); ((p - 1)/2) × 8m
+(0, 0, (u/p)) +(0, 0, (u/p)) 4f(e‡ ); ((p - 1)/2) × 8m p × 4g p × 8h 8i(j† ); ((p - 1)/2) × 16n 8j(i† ); ((p - 1)/2) × 16n
p = prime > 2; 8k(l‡ ); ((p - 1)/2) × 16n 8l(k‡ ); p × 8m p × 16n
u = 1, . . ., p - 1 ((p - 1)/2) × 16n
[9] P42/nnm 3a, 3b, c (1/3)x, (1/3)y, z; (1/3)x, (1/3)y, z; 2a(b*); 8i(j*); 8m 2b(a*); 8j(i*); 8m 4c; 8i; 8j; 16n 4d; 8k; 8l; 16n 4e; 8l; 8m; 16n
±((1/3), 0, 0); ±(0, (1/3), 0); 4f; 8k; 8m; 16n 4g; 2 × 8m; 16n 8h; 4 × 16n 3 × 8i(j*); 3 × 16n 3 × 8j(i*); 3 × 16n
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) 3 × 8k; 3 × 16n 3 × 8l; 3 × 16n 3 × 8m; 3 × 16n 9 × 16n
[p2] P42/nnm pa, pb, c (1/p)x, (1/p)y, z; (1/p)x, (1/p)y, z; 2a(b† ); ((p - 1)/2) × 8i(j† ); 2b(a† ); ((p - 1)/2) × 8j(i† ); 4c; ((p - 1)/2) × 8i; 4d; ((p - 1)/2) × 8k; 4e; ((p - 1)/2) × 8l;
+((u/p), (v/p), 0) +((u/p), (v/p), 0) ((p - 1)/2) × 8m; ((p - 1)/2) × 8m; ((p - 1)/2) × 8j; ((p - 1)/2) × 8l; ((p - 1)/2) × 8m;
p = prime > 2; (((p - 1)(p - 3))/8) × 16n (((p - 1)(p - 3))/8) × 16n (((p - 1)2)/4) × 16n (((p - 1)2)/4) × 16n (((p - 1)2)/4) × 16n
u, v = 1, . . ., p - 1
4f; ((p - 1)/2) × 8k; 4g; (p - 1) × 8m; 8h; ((p2 - 1)/2) × 16n p × 8i(j† ); p × 8j(i† );
((p - 1)/2) × 8m; (((p - 1)2)/4) × 16n ((p(p - 1))/2) × 16n ((p(p - 1))/2) × 16n
(((p - 1)2)/4) × 16n
p × 8k; ((p(p - 1))/2) × 16n p × 8l; p × 8m; p2 × 16n
((p(p - 1))/2) × 16n ((p(p - 1))/2) × 16n
* origin 2
† origin 2 and p = 4n - 1
‡ origin 1 and p = 4n - 1









































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