Origin on 41g

Asymmetric unit

0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; y ≤ 1/2 - x

(1)  1	(2)  2   0, 0, z	(3)  4+   0, 0, z	(4)  4-   0, 0, z
(5)  a   x, 1/4, z	(6)  b   1/4, y, z	(7)  m   x +1/2, -x, z	(8)  g(1/2, 1/2, 0)   x, x, z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter, Site symmetry	Coordinates	Reflection conditions
		General:
8 d 1	(1) x, y, z (2) -x, -y, z (3) -y, x, z (4) y, -x, z (5) x + 1/2, -y + 1/2, z (6) -x + 1/2, y + 1/2, z (7) -y + 1/2, -x + 1/2, z (8) y + 1/2, x + 1/2, z	0k: k = 2n h0: h = 2n

		Special: as above, plus
4 c  . . m	x, x + 1/2, z -x, -x + 1/2, z -x + 1/2, x, z x + 1/2, -x, z	no extra conditions
2 b  2 . mm	1/2, 0, z 0, 1/2, z	hk: h + k = 2n
2 a  4 . .	0, 0, z 1/2, 1/2, z	hk: h + k = 2n

Symmetry of special projections

Along [001]   p4gm a' = a   b' = b    Origin at 0, 0, z

Along [100]   1m1 a' = 1/2b    Origin at x, 0, 0

Along [110]   1m1 a' = 1/2(-a + b)    Origin at x, x, 0

Maximal non-isotypic subgroups

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I	[2] p411 (p4, 49)	1; 2; 3; 4
	[2] p21m (cmm2, 26)	1; 2; 7; 8
	[2] p2b1 (pba2, 25)	1; 2; 5; 6

IIa

none

IIb

none

Maximal isotypic subgroups of lowest index

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IIc	[9] p4bm (a' = 3a, b' = 3b) (56)

Minimal non-isotypic supergroups

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I	[2] p4/nbm (62); [2] p4/mbm (63)

II	[2] c4mm (p4mm, 55)

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