Origin at 321

Asymmetric unit	0 ≤ x ≤ 2/3; 0 ≤ y ≤ 2/3; x ≤ (1 + y)/2; y ≤ min(1 - x, (1 + x)/2); 0 ≤ z
Vertices	0, 0   1/2, 0   2/3, 1/3   1/3, 2/3   0, 1/2

(1)  1	(2)  3+   0, 0, z	(3)  3-   0, 0, z
(4)  2   x, x, 0	(5)  2   x, 0, 0	(6)  2   0, y, 0

Generators selected (1); t(1, 0, 0); t(0, 1, 0); (2); (4)

Positions

Multiplicity, Wyckoff letter, Site symmetry	Coordinates	Reflection conditions
		General:
6 e 1	(1) x, y, z (2) -y, x - y, z (3) -x + y, -x, z (4) y, x, -z (5) x - y, -y, -z (6) -x, -x + y, -z	no conditions

		Special: no extra conditions
3 d  . 2 .	x, 0, 0 0, x, 0 -x, -x, 0
2 c  3 . .	1/3, 2/3, z 2/3, 1/3, -z
2 b  3 . .	0, 0, z 0, 0, -z
1 a  3 2 .	0, 0, 0

Symmetry of special projections

Along [001]   p31m a' = a   b' = b    Origin at 0, 0, z

Along [100]   211 a' = 1/2(a + 2b)    Origin at x, 0, 0

Along [210]   11m a' = 1/2b    Origin at x, 1/2x, 0

Maximal non-isotypic subgroups

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I	[2] p311 (p3, 65)	1; 2; 3
	[3] p121 (c211, 10)	1; 4
	[3] p121 (c211, 10)	1; 5
	[3] p121 (c211, 10)	1; 6

IIa

none

IIb	[3] h321 (a' = 3a, b' = 3b) (p312, 67)

Maximal isotypic subgroups of lowest index

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IIc	[4] p321 (a' = 2a, b' = 2b) (68)

Minimal non-isotypic supergroups

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I	[2] p-3m1 (72); [2] p622 (76); [2] p-62m (79)

II	[2] h321 (p312, 67)

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