| P213 | T4 | 23 | Cubic  |
| No. 198 | P213 | Patterson symmetry Pm-3 | |
Origin on 3[111] at midpoint of three non-intersecting pairs of parallel 21 axes
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; -1/2 ≤ z ≤ 1/2; max(x - 1/2, -y) ≤ z ≤ min(x, y) | ||||||
| Vertices |
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Symmetry operations
| (1) 1 | (2) 2(0, 0, 1/2) 1/4, 0, z | (3) 2(0, 1/2, 0) 0, y, 1/4 | (4) 2(1/2, 0, 0) x, 1/4, 0 |
| (5) 3+ x, x, x | (6) 3+ -x + 1/2, x, -x | (7) 3+ x + 1/2, -x - 1/2, -x | (8) 3+ -x, -x + 1/2, x |
| (9) 3- x, x, x | (10) 3-(-1/3, 1/3, 1/3) x + 1/6, -x + 1/6, -x | (11) 3-(1/3, 1/3, -1/3) -x + 1/3, -x + 1/6, x | (12) 3-(1/3, -1/3, 1/3) -x - 1/6, x + 1/3, -x |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||||||||||||
| h, k, l cyclically permutable General: | |||||||||||||||||
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| h00 : h = 2n |
| Special: as above, plus | |||||||||
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| no extra conditions |
Symmetry of special projections
| Along [001] p2gg a' = a b' = b Origin at 1/4, 0, z | Along [111] p3 a' = 1/3(2a - b - c) b' = 1/3(-a + 2b - c) Origin at x, x, x | Along [110] p1g1 a' = 1/2(-a + b) b' = c Origin at x + 1/4, x, 0 |
Maximal non-isomorphic subgroups
| I | [3] P211 (P212121, 19) | 1; 2; 3; 4 | ||||||||||||||
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![[brace]](/graphics/sg/brace4.gif)
| IIa | none |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [27] P213 (a' = 3a, b' = 3b, c' = 3c) (198) |
Minimal non-isomorphic supergroups
| I | [2] Pa-3 (205); [2] P4332 (212); [2] P4132 (213) |
| II | [2] I213 (199); [4] F23 (196) |
