Pban No. 50 P2/b2/a2/n D2h4


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] Pba2 (32) x + (1/4), y + (1/4), z 2a 2b 2b 2a 4c 4c 4c 4c 4c 4c
2 × 2a 2 × 2b 2 × 4c
[2] P2an (30) x, y + (1/4), z 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 4c 4c
[conventional setting]Pnc2 c, b, -a z, y, -x z, y + (1/4), -x 4c 4c 2 × 4c
[2] Pb2n (30) x + (1/4), y, z 2a 2a 2b 2b 4c 4c 4c 4c 2 × 2a 2 × 2b
[conventional setting]Pnc2 c, a, b z, x, y z, x + (1/4), y 4c 4c 2 × 4c
[2] P222 (16) x + (1/4), y + (1/4), z 1a; 1e 1b; 1c 1f; 1g 1d; 1h 4u 4u 2i; 2k 2j; 2l 2m; 2o 2n; 2p
2q; 2t 2r; 2s 2 × 4u
[2] P2/b11 (13) x + (1/4), y + (1/4), z 2e 2e 2f 2f 2a; 2c 2b; 2d 2 × 2e 2 × 2f 4g 4g
[conventional setting]P12/c1 c, a, b z, x + (1/4), y + (1/4) z, x, y 4g 4g 2 × 4g
[2] P12/a1 (13) x + (1/4), y + (1/4), z 2e 2e 2f 2f 2a; 2c 2b; 2d 4g 4g 2 × 2e 2 × 2f
[conventional setting]P12/c1 -c, b, a -z, y + (1/4), x + (1/4) -z, y, x 4g 4g 2 × 4g
[2] P112/n (13) x + (1/4), y + (1/4), z 2e 2f 2f 2e 2a; 2d 2b; 2c 4g 4g 4g 4g
2 × 2e 2 × 2f 2 × 4g
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Pnan (52) a, b, 2c x + (1/4), y + (1/4), (1/2)z; x, y, (1/2)z; 4c 4c 4d 4d 4a; 4b 8e 8e 2 × 4d 2 × 4c 8e
+(0, 0, (1/2)) +(0, 0, (1/2)) 8e 8e 2 × 8e
[conventional setting]Pnna a, -2c, b x + (1/4), -(1/2)z, y + (1/4); x, -(1/2)z, y;
+(0, (1/2), 0) +(0, (1/2), 0)
[2] Pnan (52) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); x, y, (1/2)z + (1/4); 4d 4d 4c 4c 8e 4a; 4b 2 × 4d 8e 8e 2 × 4c
+(0, 0, (1/2)) +(0, 0, (1/2)) 8e 8e 2 × 8e
[conventional setting]Pnna a, -2c, b x + (1/4), -(1/2)z - (1/4), y + (1/4); x, -(1/2)z - (1/4), y;
+(0, (1/2), 0) +(0, (1/2), 0)
[2] Pbnn (52) a, b, 2c x + (1/4), y + (1/4), (1/2)z; x, y, (1/2)z; 4c 4c 4d 4d 4a; 4b 8e 2 × 4c 8e 8e 2 × 4d
+(0, 0, (1/2)) +(0, 0, (1/2)) 8e 8e 2 × 8e
[conventional setting]Pnna b, 2c, a y + (1/4), (1/2)z, x + (1/4); y, (1/2)z, x;
+(0, (1/2), 0) +(0, (1/2), 0)
[2] Pbnn (52) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); x, y, (1/2)z + (1/4); 4d 4d 4c 4c 8e 4a; 4b 8e 2 × 4c 2 × 4d 8e
+(0, 0, (1/2)) +(0, 0, (1/2)) 8e 8e 2 × 8e
[conventional setting]Pnna b, 2c, a y + (1/4), (1/2)z + (1/4), x + (1/4); y, (1/2)z + (1/4), x;
+(0, (1/2), 0) +(0, (1/2), 0)
[2] Pnnn (48) a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z; 4k 4l 2b; 2d 2a; 2c 4e; 4f 8m 8m 4g; 4h 8m 4i; 4j
+(0, 0, (1/2)) +(0, 0, (1/2)) 2 × 4k 2 × 4l 2 × 8m
[2] Pnnn (48) a, b, 2c x, y, (1/2)z; x, y, (1/2)z + (1/4); 2a; 2c 2b; 2d 4l 4k 8m 4e; 4f 4g; 4h 8m 4i; 4j 8m
+(0, 0, (1/2)) +(0, 0, (1/2)) 2 × 4k 2 × 4l 2 × 8m


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


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
Pncb a→ b → c → a a→ b → c → a x→ y → z → x
Pcna a← b ← c ← a a← b ← c ← a x← y ← z ← x









































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