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) xy(2) -yx - 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 + 2b2/31/3
h3 (13, p3)<2 + (1, 1)>a - b, a + 2b1/32/3

[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, pbuv
 p prime; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for p = 2 or p = 6n - 1

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


p3 (13)<2 + (u, -u)>qa - rb, ra + (q + r)bu, 0
 prime p = 6n + 1; 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








































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