Origin on 31m

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

(1)  1	(2)  3+   0, 0, z	(3)  3-   0, 0, z
(4)  m   x, x, z	(5)  m   x, 0, z	(6)  m   0, y, 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 d 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 c  . . m	x, 0, z 0, x, z -x, -x, z
2 b  3 . .	1/3, 2/3, z 2/3, 1/3, z
1 a  3 . m	0, 0, z

Symmetry of special projections

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

Along [100]   1m1 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

---

I	[2] p311 (p3, 65)	1; 2; 3
	[3] p11m (cm11, 13)	1; 4
	[3] p11m (cm11, 13)	1; 5
	[3] p11m (cm11, 13)	1; 6

IIa

none

IIb	[3] h31m (a' = 3a, b' = 3b) (p3m1, 69)

Maximal isotypic subgroups of lowest index

---

IIc	[4] p31m (a' = 2a, b' = 2b) (70)

Minimal non-isotypic supergroups

---

I	[2] p-31m (71); [2] p6mm (77); [2] p-62m (79)

II	[2] h31m (p3m1, 69)

---