Pmm2 No. 25 C2v1


Axes Coordinates Wyckoff positions
1a 1b 1c 1d 2e 2f 2g 2h 4i
I Maximal translationengleiche subgroups
[2] Pm11 (6) 1a 1a 1b 1b 2c 2c 2 × 1a 2 × 1b 2 × 2c
[conventional setting]P1m1 c, a, b z, x, y
[2] P1m1 (6) 1a 1b 1a 1b 2 × 1a 2 × 1b 2c 2c 2 × 2c
[2] P112 (3) 1a 1c 1b 1d 2e 2e 2e 2e 2 × 2e
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] Fmm2 (42) 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 2 × 4a 8c 8d 8b 2 × 8d 16e 2 × 8c 16e 2 × 16e
[2] Fmm2 (42) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y, (1/2)z; +((1/2), 0, 0) 8d 8b 2 × 4a 8c 2 × 8d 16e 16e 2 × 8c 2 × 16e
[2] Fmm2 (42) 2a, 2b, 2c (1/2)x, (1/2)y + (1/4), (1/2)z; +((1/2), 0, 0) 8c 2 × 4a 8b 8d 16e 2 × 8d 2 × 8c 16e 2 × 16e
[2] Fmm2 (42) 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z; +((1/2), 0, 0) 8b 8d 8c 2 × 4a 16e 2 × 8d 16e 2 × 8c 2 × 16e
[2] Aem2 (39) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, (1/2), 0) 4a 4c 4b 4c 8d 2 × 4c 8d 8d 2 × 8d
[2] Aem2 (39) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 4c 4a 4c 4b 2 × 4c 8d 8d 8d 2 × 8d
[2] Bme2 (39) 2a, b, 2c (1/2)x, y, (1/2)z; +((1/2), 0, 0) 4a 4b 4c 4c 8d 8d 8d 2 × 4c 2 × 8d
[conventional setting]Aem2 -b, 2a, 2c -y, (1/2)x, (1/2)z; +(0, (1/2), 0)
[2] Bme2 (39) 2a, b, 2c (1/2)x + (1/4), y, (1/2)z; +((1/2), 0, 0) 4c 4c 4a 4b 8d 8d 2 × 4c 8d 2 × 8d
[conventional setting]Aem2 -b, 2a, 2c -y, (1/2)x + (1/4), (1/2)z; +(0, (1/2), 0)
[2] Amm2 (38) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, (1/2), 0) 2 × 2a 4d 2 × 2b 4e 2 × 4c 8f 2 × 4d 2 × 4e 2 × 8f
[2] Amm2 (38) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 4d 2 × 2a 4e 2 × 2b 8f 2 × 4c 2 × 4d 2 × 4e 2 × 8f
[2] Bmm2 (38) 2a, b, 2c (1/2)x, y, (1/2)z; +(0, 0, (1/2)) 2 × 2a 2 × 2b 4d 4e 2 × 4d 2 × 4e 2 × 4c 8f 2 × 8f
[conventional setting]Amm2 -b, 2a, 2c -y, (1/2)x, (1/2)z; +(0, (1/2), 0)
[2] Bmm2 (38) 2a, b, 2c (1/2)x + (1/4), y, (1/2)z; +(0, 0, (1/2)) 4d 4e 2 × 2a 2 × 4b 2 × 4d 2 × 4e 8f 2 × 4c 2 × 8f
[conventional setting]Amm2 -b, 2a, 2c -y, (1/2)x + (1/4), (1/2)z; +(0, (1/2), 0)
[2] Cmm2 (35) 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0) 2a; 2b 4e 4d 4c 2 × 4d 8f 2 × 4e 8f 2 × 8f
[2] Cmm2 (35) 2a, 2b, c (1/2)x + (1/4), (1/2)y, z; +((1/2), 0, 0) 4d 4c 2a; 2b 4e 2 × 4d 8f 8f 2 × 4e 2 × 8f
[2] Cmm2 (35) 2a, 2b, c (1/2)x, (1/2)y + (1/4), z; +((1/2), 0, 0) 4e 2a; 2b 4c 4d 8f 2 × 4d 2 × 4e 8f 2 × 8f
[2] Cmm2 (35) 2a, 2b, c (1/2)x + (1/4), (1/2)y + (1/4), z; +((1/2), 0, 0) 4c 4d 4e 2a; 2b 8f 2 × 4d 8f 2 × 4e 2 × 8f
[2] Pma2 (28) 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a 2b 2c 2c 4d 4d 4d 2 × 2c 2 × 4d
[2] Pma2 (28) 2a, b, c (1/2)x + (1/4), y, z; +((1/2), 0, 0) 2c 2c 2a 2b 4d 4d 2 × 2c 4d 2 × 4d
[2] Pbm2 (28) a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a 2c 2b 2c 4d 2 × 2c 4d 4d 2 × 4d
[conventional setting]Pma2 2b, -a, c (1/2)y, -x, z; +((1/2), 0, 0)
[2] Pbm2 (28) a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 2c 2a 2c 2b 2 × 2c 4d 4d 4d 2 × 4d
[conventional setting]Pma2 2b, -a, c (1/2)y + (1/4), -x, z; +((1/2), 0, 0)
[2] Pcc2 (27) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2b 2c 2d 4e 4e 4e 4e 2 × 4e
[2] Pmc21(26) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 2 × 4c
[2] Pcm21(26) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a 2b 2a 2b 2 × 2a 2 × 2b 4c 4c 2 × 4c
[conventional setting]Pmc21 b, -a, 2c y, -x, (1/2)z; +(0, 0, (1/2))
   Enlarged unit cell, isomorphic
[2] Pmm2 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 1a; 1c 1b; 1d 2e 2f 2 × 2e 2 × 2f 2g; 2h 4i 2 × 4i
[2] Pmm2 2a, b, c (1/2)x + (1/4), y, z; +((1/2), 0, 0) 2e 2f 1a; 1c 1b; 1d 2 × 2e 2 × 2f 4i 2g; 2h 2 × 4i
[3] Pmm2 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 1a; 2e 1b; 2f 1c; 2e 1d; 2f 3 × 2e 3 × 2f 2g; 4i 2h; 4i 3 × 4i
[p] Pmm2 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 1a; 1b; 1c; 1d; p × 2e p × 2f 2g; 2h; p × 4i
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 2e ((p - 1)/2) × 2f ((p - 1)/2) × 2e ((p - 1)/2) × 2f ((p - 1)/2) × 4i ((p - 1)/2) × 4i
[2] Pmm2 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 1a; 1b 2g 1c; 1d 2h 2e; 2f 4i 2 × 2g 2 × 2h 2 × 4i
[2] Pmm2 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 2g 1a; 1b 2h 1c; 1d 4i 2e; 2f 2 × 2g 2 × 2h 2 × 4i
[3] Pmm2 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 1a; 2g 1b; 2g 1c; 2h 1d; 2h 2e; 4i 2f; 4i 3 × 2g 3 × 2h 3 × 4i
[p] Pmm2 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 1a; 1b; 1c; 1d; 2e; 2f; p × 2g p × 2h p × 4i
p = prime > 2; u = 1, . . ., p - 1 ((p - 1)/2) × 2g ((p - 1)/2) × 2g ((p - 1)/2) × 2h ((p - 1)/2) × 2h ((p - 1)/2) × 4i ((p - 1)/2) × 4i
[2] Pmm2 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 1a 2 × 1b 2 × 1c 2 × 1d 2 × 2e 2 × 2f 2 × 2g 2 × 2h 2 × 4i
[3] Pmm2 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 1a 3 × 1b 3 × 1c 3 × 1d 3 × 2e 3 × 2f 3 × 2g 3 × 2h 3 × 4i
[p] Pmm2 a, b, pc x, y, (1/p)y, z; +(0, 0, (u/p)) p × 1a p × 1b p × 1c p × 1d p × 2e p × 2f p × 2g p × 2h p × 4i
p = prime; u = 1, . . ., p - 1


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
P2mm A→ B → C → A a→ b → c → a a→ b → c → a x→ y → z → x
Pm2m A← B ← C ← A a← b ← c ← a a← b ← c ← a x← y ← z ← x









































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