Pmma No. 51 P21/m2/m2/a D2h5


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g 4h 4i 4j
4k 8l
I Maximal translationengleiche subgroups
[2] Pm2a (28) 2a 2a 2b 2b 2c 2c 2 × 2a 2 × 2b 4d 4d
[conventional setting]Pma2 a, c, -b x, z, -y 2 × 2c 2 × 4d
[2] P21ma (26) 2a 2b 2a 2b 2a 2b 4c 4c 2 × 2a 2 × 2b
[conventional setting]Pmc21 b, c, a y, z, x 4c 2 × 4c
[2] Pmm2 (25) x + (1/4), y, z 2e 2f 2e 2f 1a; 1c 1b; 1d 4i 4i 2 × 2e 2 × 2f
2g; 2h 2 × 4i
[2] P2122 (17) 2a 2a 2b 2b 2c 2d 2 × 2a 2 × 2b 4e 4e
[conventional setting]P2221 b, c, a y, z, x 4e 2 × 4e
[2] P112/a (13) 2a 2d 2c 2b 2e 2f 4g 4g 4g 4g
[conventional setting]P12/c1 b, c, a y, z, x 4g 2 × 4g
[2] P21/m11 (11) 2a 2c 2b 2d 2e 2e 4f 4f 4f 4f
[conventional setting]P121/m1 c, a, b z, x, y 2 × 2e 2 × 4f
[2] P12/m1 (10) 1a; 1d 1b; 1e 1c; 1g 1f; 1h 2m 2n 2i; 2j 2k; 2l 2 × 2m 2 × 2n
4o 2 × 4o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Aema (64) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, (1/2), 0) 4a; 4b 8d 8f 8c 8f 8e 2 × 8d 16g 2 × 8f 16g
[conventional setting]Cmce 2b, 2c, a (1/2)y, (1/2)z, x; +((1/2), 0, 0) 16g 2 × 16g
[2] Aema (64) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 8d 4a; 4b 8c 8f 8e 8f 2 × 8d 16g 16g 2 × 8f
[conventional setting]Cmce 2b, 2c, a (1/2)y + (1/4), (1/2)z, x; +((1/2), 0, 0) 16g 2 × 16g
[2] Aema (64) a, 2b, 2c x, (1/2)y, (1/2)z + (1/4); +(0, (1/2), 0) 8f 8c 4a; 4b 8d 8f 8e 16g 2 × 8d 2 × 8f 16g
[conventional setting]Cmce 2b, 2c, a (1/2)y, (1/2)z + (1/4), x; +((1/2), 0, 0) 16g 2 × 16g
[2] Aema (64) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z + (1/4); +(0, (1/2), 0) 8c 8f 8d 4a; 4b 8e 8f 16g 2 × 8d 16g 2 × 8f
[conventional setting]Cmce 2b, 2c, a (1/2)y + (1/4), (1/2)z + (1/4), x; +((1/2), 0, 0) 16g 2 × 16g
[2] Amma (63) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, (1/2), 0) 4a; 4b 8e 8f 8d 2 × 4c 8g 2 × 8e 16h 2 × 8f 16h
[conventional setting]Cmcm 2b, 2c, a (1/2)y, (1/2)z, x; +((1/2), 0, 0) 2 × 8g 2 × 16h
[2] Amma (63) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 8e 4a; 4b 8d 8f 8g 2 × 4c 2 × 8e 16h 16h 2 × 8f
[conventional setting]Cmcm 2b, 2c, a (1/2)y + (1/4), (1/2)z, x; +((1/2), 0, 0) 2 × 8g 2 × 16h
[2] Amma (63) a, 2b, 2c x, (1/2)y, (1/2)z + (1/4); +(0, (1/2), 0) 8f 8d 4a; 4b 8e 2 × 4c 8g 16h 2 × 8e 2 × 8f 16h
[conventional setting]Cmcm 2b, 2c, a (1/2)y, (1/2)z + (1/4), x; +((1/2), 0, 0) 2 × 8g 2 × 16h
[2] Amma (63) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z + (1/4); +(0, (1/2), 0) 8d 8f 8e 4a; 4b 8g 2 × 4c 16h 2 × 8e 16h 2 × 8f
[conventional setting]Cmcm 2b, 2c, a (1/2)y + (1/4), (1/2)z + (1/4), x; +((1/2), 0, 0) 2 × 8g 2 × 16h
[2] Pmmn (59) a, 2b, c origin 1 : x + (1/4), (1/2)y + (1/4), z; +(0, (1/2), 0) 4c 4f 4d 4f 4e 2a; 2b 8g 8g 8g 2 × 4f
origin 2 : x, (1/2)y, z; +(0, (1/2), 0) 2 × 4e 2 × 8g
[2] Pmmn (59) a, 2b, c origin 1 : x + (1/4), (1/2)y, z; +(0, (1/2), 0) 4f 4c 4f 4d 2a; 2b 4e 8g 8g 2 × 4f 8g
origin 2 : x, (1/2)y + (1/4), z; +(0, (1/2), 0) 2 × 4e 2 × 8g
[2] Pbma (57) a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 4a 4d 4b 4d 4c 4d 8e 8e 8e 2 × 4d
[conventional setting] Pbcm c, a, 2b z, x, (1/2)y; +(0, 0, (1/2)) 8e 2 × 8e
[2] Pbma (57) a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4d 4a 4d 4b 4d 4c 8e 8e 2 × 4d 8e
[conventional setting] Pbcm c, a, 2b z, x, (1/2)y + (1/4); +(0, 0, (1/2)) 8e 2 × 8e
[2] Pmca (57) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a 4b 4c 4c 4d 4d 8e 2 × 4c 8e 8e
[conventional setting] Pbcm b, 2c, a y, (1/2)z, x; +(0, (1/2), 0) 2 × 4d 2 × 8e
[2] Pmca (57) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c 4c 4a 4b 4d 4d 2 × 4c 8e 8e 8e
[conventional setting] Pbcm b, 2c, a y, (1/2)z + (1/4), x; +(0, (1/2), 0) 2 × 4d 2 × 8e
[2] Pcma (55) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 2b; 2d 4g 4h 4g 4h 4e; 4f 8i 2 × 4g 2 × 4h
[conventional setting] Pbam 2c, a, b (1/2)z, x, y; +((1/2), 0, 0) 8i 2 × 8i
[2] Pcma (55) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4g 4h 2a; 2c 2b; 2d 4g 4h 8i 4e; 4f 2 × 4g 2 × 4h
[conventional setting] Pbam 2c, a, b (1/2)z + (1/4), x, y; +((1/2), 0, 0) 8i 2 × 8i
[2] Pcca (54) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 4a 4b 4c 4c 4d 4e 8f 2 × 4c 8f 8f
8f 2 × 8f
[2] Pcca (54) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c 4c 4a 4b 4d 4e 2 × 4c 8f 8f 8f
8f 2 × 8f
[2] Pbmn (53) a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2b 4e 2c; 2d 4f 4h 4g 2 × 4e 2 × 4f 2 × 4h 8i
[conventional setting] Pmna 2b, c, a (1/2)y, z, x; +((1/2), 0, 0) 8i 2 × 8i
[2] Pbmn (53) a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4e 2a; 2b 4f 2c; 2d 4g 4h 2 × 4e 2 × 4f 8i 2 × 4h
[conventional setting] Pmna 2b, c, a (1/2)y + (1/4), z, x; +((1/2), 0, 0) 8i 2 × 8i
   Enlarged unit cell, isomorphic
[3] Pmma 3a, b, c (1/3)x, y, z; 2a; 4i 2b; 4j 2c; 4i 2d; 4j 2e; 4i 2f; 4j 4g; 8l 4h; 8l 3 × 4i 3 × 4j
±((1/3), 0, 0) 4k; 8l 3 × 8l
[p] Pmma pa, b, c (1/p)x, y, z; 2a; 2b; 2c; 2d; 2e; 2f; 4g; 4h; p × 4i p × 4j
+((u/p), 0, 0) ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 8l ((p - 1)/2) × 8l
p = prime > 2; u = 1, . . ., p - 1 4k; p × 8l
((p - 1)/2) × 8l
[2] Pmma a, 2b, c x, (1/2)y, z; 2a; 2b 4g 2c; 2d 4h 2e; 2f 4k 2 × 4g 2 × 4h 4i; 4j 8l
+(0, (1/2), 0) 2 × 4k 2 × 8l
[2] Pmma a, 2b, c x, (1/2)y + (1/4), z; 4g 2a; 2b 4h 2c; 2d 4k 2e; 2f 2 × 4g 2 × 4h 8l 4i; 4j
+(0, (1/2), 0) 2 × 4k 2 × 8l
[3] Pmma a, 3b, c x, (1/3)y, z; 2a; 4g 2b; 4g 2c; 4h 2d; 4h 2e; 4k 2f; 4k 3 × 4g 3 × 4h 4i; 8l 4j; 8l
±(0, (1/3), 0) 3 × 4k 3 × 8l
[p] Pmma a, pb, c x, (1/p)y, z; 2a; 2b; 2c; 2d; 2e; 2f; p × 4g p × 4h 4i; 4j;
+(0, (u/p), 0) ((p - 1)/2) × 4g ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 4k ((p - 1)/2) × 4k ((p - 1)/2) × 8l ((p - 1)/2) × 8l
p = prime > 2; u = 1, . . ., p - 1 p × 4k p × 8l
[2] Pmma a, b, 2c x, y, (1/2)z; 2a; 2c 2b; 2d 4i 4j 2 × 2e 2 × 2f 4g; 4h 8l 2 × 4i 2 × 4j
+(0, 0, (1/2)) 2 × 4k 2 × 8l
[2] Pmma a, b, 2c x, y, (1/2)z + (1/4); 4i 4j 2a; 2c 2b; 2d 2 × 2e 2 × 2f 8l 4g; 4h 2 × 4i 2 × 4j
+(0, 0, (1/2)) 2 × 4k 2 × 8l
[3] Pmma a, b, 3c x, y, (1/3)z; 2a; 4i 2b; 4j 2c; 4i 2d; 4j 3 × 2e 3 × 2f 4g; 8l 4h; 8l 3 × 4i 3 × 4j
±(0, 0, (1/3)) 3 × 4k 3 × 8l
[p] Pmma a, b, pc x, y, (1/p)z; 2a; 2b; 2c; 2d; p × 2e p × 2f 4g; 4h; p × 4i p × 4j
+(0, 0, (u/p)) ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 8l ((p - 1)/2) × 8l
p = prime > 2; u = 1, . . ., p - 1 p × 4k p × 8l


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
Pbmm A → B; C → A a→ b → c → a a→ b → c → a x→ y → z → x
Pmcm A → C; C → B a← b ← c ← a a← b ← c ← a x← y ← z ← x
Pmmb A→ B a<-> b a<-> -b x<-> -y
Pcmm A<-> C a<-> c a<-> -c x<-> -z
Pmam C→ B b<-> c b<-> -c y<-> -z









































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