P213 T4 23 Cubic info
No. 198 P213 Patterson symmetry Pm-3

symmetry group diagram

Origin on 3[111] at midpoint of three non-intersecting pairs of parallel 21 axes

Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; -1/2 ≤ z ≤ 1/2; max(x - 1/2, -y) ≤ z ≤ min(xy)
Vertices
0, 0, 0  1/2, 0, 0  1/21/2, 0  0, 1/2, 0  1/21/21/2  0, 1/2, -1/2  

Symmetry operations

(1)  1   (2)  2(0, 0, 1/2)   1/4, 0, z(3)  2(0, 1/2, 0)   0, y1/4(4)  2(1/2, 0, 0)   x1/4, 0
(5)  3+   xxx(6)  3+   -x + 1/2x-x(7)  3+   x + 1/2-x - 1/2-x(8)  3+   -x-x + 1/2x
(9)  3-   xxx(10)  3-(-1/31/31/3)   x + 1/6-x + 1/6-x(11)  3-(1/31/3, -1/3)   -x + 1/3-x + 1/6x(12)  3-(1/3, -1/31/3)   -x - 1/6x + 1/3-x

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 h, k, l cyclically permutable
General:
12 b 1
(1) xyz(2) -x + 1/2-yz + 1/2(3) -xy + 1/2-z + 1/2(4) x + 1/2-y + 1/2-z
(5) zxy(6) z + 1/2-x + 1/2-y(7) -z + 1/2-xy + 1/2(8) -zx + 1/2-y + 1/2
(9) yzx(10) -yz + 1/2-x + 1/2(11) y + 1/2-z + 1/2-x(12) -y + 1/2-zx + 1/2
h00: h = 2n
    Special: as above, plus
4 a  . 3 . 
xxx -x + 1/2-xx + 1/2 -xx + 1/2-x + 1/2x + 1/2-x + 1/2-x
no extra conditions

Symmetry of special projections

Along [001]   p2gg
a' = a   b' = b   
Origin at 1/4, 0, z
Along [111]   p3
a' = 1/3(2a - b - c)   b' = 1/3(-a + 2b - c)   
Origin at xxx
Along [110]   p1g1
a' = 1/2(-a + b)   b' = c   
Origin at x + 1/4x, 0








































to end of page
to top of page