p3 No. 13 p3

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

General position

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates
 
3 d 1
(1) x, y(2) -y, x - y(3) -x + y, -x

I Maximal translationengleiche subgroups

[3] p1 (1)1

II Maximal klassengleiche subgroups

[3] a' = 3a, b' = 3b

h3 (13, p3)<2>a - b, a + 2b
h3 (13, p3)<2 + (1, 0)>a - b, a + 2b2/3, 1/3
h3 (13, p3)<2 + (1, 1)>a - b, a + 2b1/3, 2/3

[4] a' = 2a, b' = 2b

bracep3 (13)<2>2a, 2b
p3 (13)<2 + (1, -1)>2a, 2b1, 0
p3 (13)<2 + (1, 2)>2a, 2b0, 1
p3 (13)<2 + (2, 1)>2a, 2b1, 1

[p2] a' = pa, b' = pb

p3 (13)<2 + (u + v, -u + 2v)>pa, pbu, v
 p > 1; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for prime p ≡ 2 (mod 3)

[p = q2 + r2 + qr] a' = qa - rb, b' = ra + (q + r)b

p3 (13)<2 + (u, -u)>qa - rb, ra + (q + r)bu, 0
 p > 6; q > 0; r > 0; 0 ≤ u < p
p conjugate subgroups for each pair of q and r

I Minimal translationengleiche supergroups

[2] p3m1 (14); [2] p31m (15); [2] p6 (16)

II Minimal non-isomorphic klassengleiche supergroups

none
none








































to end of page
to top of page