Origin on 3

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

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

Positions

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

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

Symmetry of special projections

Along [001]   p3 a' = a   b' = b    Origin at 0, 0, z

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

Along [210]   111 a' = 1/2b    Origin at x, 1/2x, 0

Maximal non-isotypic subgroups

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I

[3] p1 (1)

1

IIa

none

IIb

none

Maximal isotypic subgroups of lowest index

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IIc	[3] h3 (a' = 3a, b' = 3b) (p3, 65)

Minimal non-isotypic supergroups

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I	[2] p-3 (66); [2] p312 (67); [2] p321 (68); [2] p3m1 (69); [2] p31m (70); [2] p6 (73); [2] p-6 (74)

II

none

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