P3m1 C3v1 3m1 Trigonal info
No. 156 P3m1 Patterson symmetry P-3m1

symmetry group diagram

Origin on 3 m 1

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

Symmetry operations

(1)  1   (2)  3+   0, 0, z(3)  3-   0, 0, z
(4)  m   x-xz(5)  m   x, 2xz(6)  m   2xxz

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (4)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
6 e 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) -y-xz(5) -x + yyz(6) xx - yz
no conditions
    Special: as above, plus
3 d  . m . 
x-xzx, 2xz (-2x), -xz
no extra conditions
1 c  3 m . 
2/31/3z
no extra conditions
1 b  3 m . 
1/32/3z
no extra conditions
1 a  3 m . 
0, 0, z
no extra conditions

Symmetry of special projections

Along [001]   p3m1
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]   p1m1
a' = 1/2b   b' = c   
Origin at x1/2x, 0








































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