Pmmn No. 59 P21/m21/m2/n D2h13


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 4c 4d 4e 4f 8g
I Maximal translationengleiche subgroups
[2] Pm21n (31) x + (1/4), y, z 2a 2a 4b 4b 2 × 2a 4b 2 × 4b
[conventional setting]Pmn21 a, c, -b x, z, -y x + (1/4), z, -y
[2] P21mn (31) x, y + (1/4), z 2a 2a 4b 4b 4b 2 × 2a 2 × 4b
[conventional setting]Pmn21 b, c, a y, z, x y + (1/4), z, x
[2] Pmm2 (25) x + (1/4), y + (1/4), z 1a; 1d 1b; 1c 4i 4i 2g; 2h 2e; 2f 2 × 4i
[2] P21212 (18) x + (1/4), y + (1/4), z 2a 2b 4c 4c 4c 4c 2 × 4c
[2] P112/n (13) x + (1/4), y + (1/4), z 2e 2f 2a; 2d 2b; 2c 4g 4g 2 × 4g
[2] P21/m11(11) x + (1/4), y + (1/4), z 2e 2e 2a; 2c 2b; 2d 2 × 2e 4f 2 × 4f
[conventional setting]P121/m1 c, a, b z, x + (1/4), y + (1/4) z, x, y
[2] P121/m1(11) x + (1/4), y + (1/4), z 2e 2e 2a; 2b 2c; 2d 4f 2 × 2e 2 × 4f
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Pcmn (62) a, b, 2c x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2)) x, y, (1/2)z; +(0, 0, (1/2)) 4c 4c 4a; 4b 8d 8d 2 × 4c 2 × 8d
[conventional setting]Pnma 2c, b, -a (1/2)z, y + (1/4), (3/4)- x; +((1/2), 0, 0) (1/2)z, y, -x; +((1/2), 0, 0)
[2] Pcmn (62) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c 4c 8d 4a; 4b 8d 2 × 4c 2 × 8d
[conventional setting]Pnma 2c, b, -a (1/2)z + (1/4), y + (1/4), (3/4)- x; +((1/2), 0, 0) (1/2)z + (1/4), y, -x; +((1/2), 0, 0)
[2] Pmcn (62) a, b, 2c x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2)) x, y, (1/2)z; +(0, 0, (1/2)) 4c 4c 4a; 4b 8d 2 × 4c 8d 2 × 8d
[conventional setting]Pnma 2c, a, b (1/2)z, x + (1/4), y + (1/4); +((1/2), 0, 0) (1/2)z, x, y; +((1/2), 0, 0)
[2] Pmcn (62) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c 4c 8d 4a; 4b 2 × 4c 8d 2 × 8d
[conventional setting]Pnma 2c, a, b (1/2)z + (1/4), x + (1/4), y + (1/4); +((1/2), 0, 0) (1/2)z + (1/4), x, y; +((1/2), 0, 0)
[2] Pccn (56) a, b, 2c x + (1/4), y + (1/4), (1/2)z; +(0, 0, (1/2)) x, y, (1/2)z; +(0, 0, (1/2)) 4c 4d 4a; 4b 8e 8e 8e 2 × 8e
[2] Pccn (56) a, b, 2c x + (1/4), y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c 4d 8e 4a; 4b 8e 8e 2 × 8e
   Enlarged unit cell, isomorphic
[3] Pmmn 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) (1/3)x, y, z; ±((1/3), 0, 0) 2a(b*); 2b(a*); 4c; 8g 4d; 8g 4e; 8g 3 × 4f 3 × 8g
4f 4f
[p] Pmmn pa, b, c (1/p)x, y, z; +((u/p), 0, 0) (1/p)x, y, z; +((u/p), 0, 0) 2a(b† ); 2b(a† ); 4c; 4d; 4e; p × 4f p × 8g
p = prime > 2;  u = 1, . . ., p - 1 ((p - 1)/2) × 4f ((p - 1)/2) × 4f ((p - 1)/2) × 8g ((p - 1)/2) × 8g ((p - 1)/2) × 8g
[3] Pmmn a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) x, (1/3)y, z; ±(0, (1/3), 0) 2a(b*); 2b(a*); 4c; 8g 4d; 8g 3 × 4e 4f; 8g 3 × 8g
4e 4e
[p] Pmmn a, pb, c x, (1/p) y, z; +(0, (u/p), 0) x, (1/p) y, z; +(0, (u/p), 0) 2a(b† ); 2b(a† ); 4c; 4d; p × 4e 4f; p × 8g
p = prime > 2;  u = 1, . . ., p - 1 ((p - 1)/2) × 4e ((p - 1)/2) × 4e ((p - 1)/2) × 8g ((p - 1)/2) × 8g ((p - 1)/2) × 8g
[2] Pmmn a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) x, y, (1/2)z; +(0, 0, (1/2)) 2 × 2a 2 × 2b 4c; 4d 8g 2 × 4e 2 × 4f 2 × 8g
[2] Pmmn a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2 × 2a 2 × 2b 8g 4c; 4d 2 × 4e 2 × 4f 2 × 8g
[3] Pmmn a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 2a 3 × 2b 4c; 8g 4d; 8g 3 × 4e 3 × 4f 3 × 8g
[p] Pmmn a, b, pc x, y, (1/p) z; +(0, 0, (u/p)) x, y, (1/p)z; +(0, 0, (u/p)) p × 2a p × 2b 4c; 4d; p × 4e; p × 4f p × 8g
p = prime > 2;  u = 1, . . ., p - 1 ((p - 1)/2) × 8g ((p - 1)/2) × 8g
 * origin 2
 † origin 2 and p = 4n - 1


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









































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