P3 C31 3 Trigonal info
No. 143 P3 Patterson symmetry P-3

symmetry group diagram

Origin on 3

Asymmetric unit 0 ≤ x ≤ 2/3; 0 ≤ y ≤ 2/3; 0 ≤ z ≤ 1; x ≤ (1 + y)/2; y ≤ min(1 - x, (1 + x)/2)
Vertices
0, 0, 0  1/2, 0, 0  2/31/3, 0  1/32/3, 0  0, 1/2, 0  
0, 0, 1  1/2, 0, 1  2/31/3, 1  1/32/3, 1  0, 1/2, 1  

Symmetry operations

(1)  1   (2)  3+   0, 0, z(3)  3-   0, 0, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
3 d 1
(1) xyz(2) -yx - yz(3) -x + y-xz
no conditions
    Special: as above, plus
1 c  3 . . 
2/31/3z
no extra conditions
1 b  3 . . 
1/32/3z
no extra conditions
1 a  3 . . 
0, 0, z
no extra conditions

Symmetry of special projections

Along [001]   p3
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   p1
a' = 1/2(a + 2b)   b' = c   
Origin at x, 0, 0
Along [210]   p1
a' = 1/2b   b' = c   
Origin at x1/2x, 0








































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