Pnnn No. 48 P2/n2/n2/n D2h2


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 2c 2d 4e 4f 4g 4h
4i 4j 4k 4l 8m
I Maximal translationengleiche subgroups
[2] P2nn (34) x, y + (1/4), z + (1/4) 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b
[conventional setting]Pnn2 b, c, a y, z, x y + (1/4), z + (1/4), x 4c 4c 4c 4c 2 × 4c
[2] Pn2n (34) x + (1/4), y, z + (1/4) 2a 2b 2b 2a 4c 4c 4c 4c
[conventional setting]Pnn2 c, a, b z, x, y z + (1/4), x + (1/4), y 2 × 2a 2 × 2b 4c 4c 2 × 4c
[2] Pnn2 (34) x + (1/4), y + (1/4), z 2a 2b 2a 2b 4c 4c 4c 4c
4c 4c 2 × 2a 2 × 2b 2 × 4c
[2] P222 (16) x + (1/4), y + (1/4), z + (1/4) 1a; 1h 1b; 1g 1d; 1e 1c; 1f 4u 4u 2i; 2l 2j; 2k
2m; 2p 2n; 2o 2q; 2t 2r; 2s 2 × 4u
[2] P2/n11 (13) x + (1/4), y + (1/4), z + (1/4) 2e 2e 2f 2f 2c; 2d 2a; 2b 2 × 2e 2 × 2f
[conventional setting]P12/n1 c, a, b z + (1/4), x + (1/4), y + (1/4) z, x, y 4g 4g 4g 4g 2 × 4g
[2] P12/n1 (13) x + (1/4), y + (1/4), z + (1/4) 2e 2f 2f 2e 2c; 2d 2a; 2b 4g 4g
2 × 2e 2 × 2f 4g 4g 2 × 4g
[2] P112/n (13) x + (1/4), y + (1/4), z + (1/4) 2e 2f 2e 2f 2c; 2d 2a; 2b 4g 4g
4g 4g 2 × 2e 2 × 2f 2 × 4g
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Fddd (70) 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); 8a; 8b 16e 16g 16f 16c; 16d 32h 2 × 16e 32h
+((1/2), 0, 0) 2 × 16f 32h 2 × 16g 32h 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y, (1/2)z; (1/2)x, (1/2)y + (1/4), (1/2)z + (1/4); 16e 8a; 8b 16f 16g 32h 16c; 16d 2 × 16e 32h
+((1/2), 0, 0) 32h 2 × 16f 32h 2 × 16g 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x, (1/2)y + (1/4), (1/2)z; (1/2)x + (1/4), (1/2)y, (1/2)z + (1/4); 16f 16g 16e 8a; 8b 32h 16c; 16d 32h 2 × 16e
+((1/2), 0, 0) 2 × 16f 32h 32h 2 × 16g 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z + (1/4); (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z; 16g 16f 8a; 8b 16e 32h 16c; 16d 32h 2 × 16e
+((1/2), 0, 0) 32h 2 × 16f 2 × 16g 32h 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x, (1/2)y + (1/4), (1/2)z + (1/4); (1/2)x + (1/4), (1/2)y, (1/2)z; 16e 8a; 8b 16f 16g 16c; 16d 32h 2 × 16e 32h
+((1/2), 0, 0) 32h 2 × 16f 32h 2 × 16g 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y, (1/2)z + (1/4); (1/2)x, (1/2)y + (1/4), (1/2)z; 16f 16g 16e 8a; 8b 16c; 16d 32h 32h 2 × 16e
+((1/2), 0, 0) 2 × 16f 32h 32h 2 × 16g 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z; (1/2)x, (1/2)y, (1/2)z + (1/4); 16g 16f 8a; 8b 16e 16c; 16d 32h 32h 2 × 16e
+((1/2), 0, 0) 32h 2 × 16f 2 × 16g 32h 2 × 32h
[2] Fddd (70) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)x, (1/2)y, (1/2)z; 8a; 8b 16e 16g 16f 32h 16c; 16d 2 × 16e 32h
(1/2)z + (1/4); 2 × 16f 32h 2 × 16g 32h 2 × 32h
+((1/2), 0, 0)
   Enlarged unit cell, isomorphic
[3] Pnnn 3a, b, c (1/3)x, y, z; (1/3)x, y, z; 2a(b*); 4g 2b(a*); 4g 2c(d*); 4h 2d(c*); 4h 4f(e*); 8m 4e(f*); 8m 3 × 4g 3 × 4h
±((1/3), 0, 0) ±((1/3), 0, 0) 4i(j*); 8m 4j(i*); 8m 4k(l*); 8m 4l(k*); 8m 3 × 8m
[p] Pnnn pa, b, c (1/p)x, y, z; (1/p)x, y, z; 2a(b† ); 2b(a† ); 2c(d† ); 2d(c† ); 4e(f‡ ); 4f(e‡ ); p × 4g p × 4h
+((u/p), 0, 0) +((u/p), 0, 0) ((p - 1)/2) × 4g ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 8m ((p - 1)/2) × 8m
p = prime > 2; u = 1, . . ., p - 1 4i(j† ); 4j(i† ); 4k(l† ); 4l(k† ); p × 8m
((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m
[3] Pnnn a, 3b, c x, (1/3)y, z; x, (1/3)y, z; 2a(d*); 4i 2b(c*); 4j 2c(b*); 4j 2d(a*); 4i 4f(e*); 8m 4e(f*); 8m 4g(h*); 8m 4h(g*); 8m
±(0, (1/3), 0) ±(0, (1/3), 0) 3 × 4i 3 × 4j 4k(l*); 8m 4l(k*); 8m 3 × 8m
[p] Pnnn a, pb, c x, (1/p)y, z; x, (1/p)y, z; 2a(d† ); 2b(c† ); 2c(b† ); 2d(a† ); 4e(f‡ ); 4f(e‡ ); 4g(h† ); 4h(g† );
+(0, (u/p), 0) +(0, (u/p), 0) ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m
p = prime > 2; u = 1, . . ., p - 1 p × 4i p × 4j 4k(l† ); 4l(k† ); p × 8m
((p - 1)/2) × 8m ((p - 1)/2) × 8m
[3] Pnnn a, b, 3c x, y, (1/3)z; x, y, (1/3)z; 2a(c*); 4k 2b(d*); 4l 2c(a*); 4k 2d(b*); 4l 4f(e*); 8m 4e(f*); 8m 4g(h*); 8m 4h(g*); 8m
±(0, 0, (1/3)) ±(0, 0, (1/3)) 4i(j*); 8m 4j(i*); 8m 3 × 4k 3 × 4l 3 × 8m
[p] Pnnn a, b, pc x, y, (1/p)z; x, y, (1/p)z; 2a(c† ); 2b(d† ); 2c(a† ); 2d(b† ); 4e(f‡ ); 4f(e‡ ); 4g(h† ); 4h(g† );
+(0, 0, (u/p)) +(0, 0, (u/p)) ((p - 1)/2) × 4k ((p - 1)/2) × 4l ((p - 1)/2) × 4k ((p - 1)/2) × 4l ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m ((p - 1)/2) × 8m
p = prime > 2; u = 1, . . ., p - 1 4i(j† ); 4j(i† ); p × 4k p × 4l p × 8m
((p - 1)/2) × 8m ((p - 1)/2) × 8m
 * origin 2  ‡ origin 1 and p = 4n - 1
 † origin 2 and p = 4n - 1









































to end of page
to top of page