Origin on 3m1

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

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

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  . m .	x, -x, z x, 2x, z -(2x), -x, z
1 c  3 m .	2/3, 1/3, z
1 b  3 m .	1/3, 2/3, z
1 a  3 m .	0, 0, z

Symmetry of special projections

Along [001]   p3m1 a' = a   b' = b    Origin at 0, 0, z

Along [100]   111 a' = 1/2(a + 2b)    Origin at x, 0, 0

Along [210]   1m1 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] p1m1 (cm11, 13)	1; 4
	[3] p1m1 (cm11, 13)	1; 5
	[3] p1m1 (cm11, 13)	1; 6

IIa

none

IIb	[3] h3m1 (a' = 3a, b' = 3b) (p31m, 70)

Maximal isotypic subgroups of lowest index

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IIc	[4] p3m1 (a' = 2a, b' = 2b) (69)

Minimal non-isotypic supergroups

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I	[2] p-3m1 (72); [2] p6mm (77); [2] p-6m2 (78)

II	[2] h3m1 (p31m, 70)

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