F-43c No. 219 Td5

 Axes Coordinates Wyckoff positions 8a 8b 24c 24d 32e 48f 48g 96h I Maximal translationengleiche subgroups [2] F23 4a; 4b 4c; 4d 24g 24f 2 × 16e 2 × 24f (196) 2 × 24g 2 × 48h [4] R3c (1/2)(b + c), (1/2)(a + c), -x + y + z, x - y + z, 2a 2a 6b 6b 2a; 6b 2 × 6b (161) (1/2)(a + b) x + y - z 2 × 6b 4 × 6b (rhombohedral axes) (1/2)(-a + b), (1/2)(-b + c), (2/3)(-2x + y + z), 6a 6a 18b 18b 6a; 18b 2 × 18b a + b + c (2/3)(-x - y + 2z), 2 × 18b 4 × 18b (hexagonal axes) (1/3)(x + y + z) conjugate: (1/2)(a + b), (1/2)(-b - c), (2/3)(2x + y - z), -a + b - c (2/3)(x - y - 2z), (hexagonal axes) (1/3)(-x + y - z) conjugate: (1/2)(-a - b), (1/2)(b - c), (2/3)(-2x - y - z), a - b - c (2/3)(-x + y - 2z), (hexagonal axes) (1/3)(x - y - z) conjugate: (1/2)(a - b), (1/2)(b + c), (2/3)(2x - y + z), -a - b + c (2/3)(x + y + 2z), (hexagonal axes) (1/3)(-x - y + z) [3] I-4c2 (1/2)(a - b), (1/2)(a + b), c x - y, x + y, z + (1/4) 4a 4d 4c; 8h 4b; 8e 16i 2 × 8e; 8f (120) 8g; 2 × 8h 3 × 16i conjugate: (1/2)(b - c), (1/2)(b + c), a y - z, y + z, x + (1/4) conjugate: (1/2)(-a + c), (1/2)(a + c), b -x + z, x + z, y + (1/4) II Maximal klassengleiche subgroups Loss of centring translations [4] P-43n 4 conjugate 2a; 6b 8e 24i 6c; 6d; 12f 8e; 24i 2 × 12f; 12g; 12h (218) subgroups 2 × 24i 4 × 24i [4] P-43n 4 conjugate x + (1/4), y + (1/4), z + (1/4) 8e 2a; 6b 6c; 6d; 12f 24i 8e; 24i 2 × 24i (218) subgroups 2 × 12f; 12g; 4 × 24i 12h Enlarged unit cell, isomorphic [27] F-43c 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 8a; 2 × 32e; 8b; 2 × 32e; 24c; 48g; 24d; 48f; 3 × 32e; 3 × 48f; ±(0, (1/3), 0); ±(0, 0, (1/3)); 48f; 96h 48g; 96h 6 × 96h 6 × 96h 8 × 96h 12 × 96h ±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); ±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); 3 × 48g; 27 × 96h ±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 12 × 96h ±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); ±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) [p3] F-43c pa, pb, pc (1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) 8a; 8b; 24c; 24d; p × 32e; p × 48f; p = prime > 2; u, v, w = 1, . . ., p - 1 (p - 1) × 32e; (p - 1) × 32e; ((p - 1)/2) × 48g; ((p - 1)/2) × 48f; ((p(p2 - 1))/3) × 96h ((p(p2 - 1))/2) × 96h ((p - 1)/2) × 48f; ((p - 1)/2) × 48g; ((p(p2 - 1))/4) × ((p(p2 - 1))/4) × ((p3 - 7p + 6)/12) × ((p3 - 7p + 6)/12) × 96h 96h 96h 96h p × 48g; p3 × 96h ((p(p2 - 1))/2) × 96h