Fd-3c No. 228 F41/d-32/c Oh8

ORIGIN CHOICE 1, Origin at 2 3, at -3/8, -3/8, -3/8 from centre (-3)

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/21/2); t(1/2, 0, 1/2); (2); (3); (5); (13); (25)

General position

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates

 (0, 0, 0)+  (0, 1/21/2)+  (1/2, 0, 1/2)+  (1/21/2, 0)+  
192 h 1
(1) xyz(2) -x-y + 1/2z + 1/2(3) -x + 1/2y + 1/2-z(4) x + 1/2-y-z + 1/2
(5) zxy(6) z + 1/2-x-y + 1/2(7) -z-x + 1/2y + 1/2(8) -z + 1/2x + 1/2-y
(9) yzx(10) -y + 1/2z + 1/2-x(11) y + 1/2-z-x + 1/2(12) -y-z + 1/2x + 1/2
(13) y + 3/4x + 1/4-z + 3/4(14) -y + 1/4-x + 1/4-z + 1/4(15) y + 1/4-x + 3/4z + 3/4(16) -y + 3/4x + 3/4z + 1/4
(17) x + 3/4z + 1/4-y + 3/4(18) -x + 3/4z + 3/4y + 1/4(19) -x + 1/4-z + 1/4-y + 1/4(20) x + 1/4-z + 3/4y + 3/4
(21) z + 3/4y + 1/4-x + 3/4(22) z + 1/4-y + 3/4x + 3/4(23) -z + 3/4y + 3/4x + 1/4(24) -z + 1/4-y + 1/4-x + 1/4
(25) -x + 3/4-y + 3/4-z + 3/4(26) x + 3/4y + 1/4-z + 1/4(27) x + 1/4-y + 1/4z + 3/4(28) -x + 1/4y + 3/4z + 1/4
(29) -z + 3/4-x + 3/4-y + 3/4 (30) -z + 1/4x + 3/4y + 1/4(31) z + 3/4x + 1/4-y + 1/4(32) z + 1/4-x + 1/4y + 3/4
(33) -y + 3/4-z + 3/4-x + 3/4(34) y + 1/4-z + 1/4x + 3/4(35) -y + 1/4z + 3/4x + 1/4(36) y + 3/4z + 1/4-x + 1/4
(37) -y-x + 1/2z(38) y + 1/2x + 1/2z + 1/2(39) -y + 1/2x-z(40) y-x-z + 1/2
(41) -x-z + 1/2y(42) x-z-y + 1/2(43) x + 1/2z + 1/2y + 1/2(44) -x + 1/2z-y
(45) -z-y + 1/2x(46) -z + 1/2y-x(47) z-y-x + 1/2(48) z + 1/2y + 1/2x + 1/2

I Maximal translationengleiche subgroups

[2] F-43c (219)(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48)+
[2] F4132 (210)(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24)+
[2] Fd-31 (203Fd-3)(1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36)+ 1/41/41/4
brace[3] F41/d12/c (142I41/acd)(1; 2; 3; 4; 13; 14; 15; 16; 25; 26; 27; 28; 37; 38; 39; 40)+1/2(a - b), 1/2(a + b), c 0, 0, 1/4
[3] F41/d12/c (142I41/acd)(1; 4; 2; 3; 18; 19; 17; 20; 25; 28; 26; 27; 42; 43; 41; 44)+1/2(b - c), 1/2(b + c), a 1/4, 0, 0
[3] F41/d12/c (142I41/acd)(1; 3; 4; 2; 22; 24; 23; 21; 25; 27; 28; 26; 46; 48; 47; 45)+1/2(-a + c), 1/2(a + c), b 0, 1/4, 0
brace[4] F1-32/c (167R-3c)(1; 5; 9; 14; 19; 24; 25; 29; 33; 38; 43; 48)+1/2(-a + b), 1/2(-b + c), a + b + c 3/83/83/8
[4] F1-32/c (167R-3c)(1; 6; 12; 13; 18; 24; 25; 30; 36; 37; 42; 48)+1/2(a + b), 1/2(-b - c), -a + b - c 1/83/81/8
[4] F1-32/c (167R-3c)(1; 7; 10; 13; 19; 22; 25; 31; 34; 37; 43; 46)+1/2(-a - b), 1/2(b - c), a - b - c 3/81/81/8
[4] F1-32/c (167R-3c)(1; 8; 11; 14; 18; 22; 25; 32; 35; 38; 42; 46)+1/2(a - b), 1/2(b + c), -a - b + c 1/81/83/8

II Maximal klassengleiche subgroups

none

none

[p3] a' = pa, b' = pb, c' = pc


Fd-3c (228)<2 + (1/2 + 2up/2 + 2vp/2 - 1/2); 3 + (p/2 + 2up/2 - 1/21/2 + 2w); 5 + (u - w, -u + v, -v + w); 13 + (3p/4 - 3/4 + u - vp/4 - 1/4 - u + v3p/4 - 1/4 + 2w); 25 + (3p/4 - 1/4 + 2u3p/4 - 1/4 + 2v3p/4 - 1/4 + 2w)>papbpc1/4 + u1/4 + v1/4 + w
 p > 2; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for prime p ≡ 3 (mod 4)
Fd-3c (228)<2 + (2up/2 - 1/2 + 2vp/2 - 1/2); 3 + (p/2 - 1/2 + 2up/2 - 1/2, 2w); 5 + (u - w, -u + v, -v + w); 13 + (3p/4 - 3/4 + u - vp/4 - 1/4 - u + v3p/4 - 3/4 + 2w); 25 + (3p/4 - 3/4 + 2u3p/4 - 3/4 + 2v3p/4 - 3/4 + 2w)>papbpcuvw
 p > 4; 0 ≤ u < p; 0 ≤ v < p; 0 ≤ w < p
p3 conjugate subgroups for prime p ≡ 1 (mod 4)

I Minimal translationengleiche supergroups

none

II Minimal non-isomorphic klassengleiche supergroups

none
[2] a' = 1/2a, b' = 1/2b, c' = 1/2c  Pn-3m (224)








































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