Symmetry properies of the D3h point group.

(if the animation doesn't start first time, click again)

1 identity
1 3-fold rotational axis
3 2-fold rotational axes
1 horizontal mirror plane
3 vertical mirror planes
3 improper rotations


Using trans-MX3Y2 as an example

 

(x axis coincident with C2 axis)
D3h
E
2C3 (z)
3C2
sigma h (xy)
2S3
3sigma v
linear functions,
quadratic
cubic functions
rotations
functions
A' 1
1
1
1
1
1
1
-
x2 +y2 , z2
x(x2 -3y2)
A' 2
1
1
-1
1
1
-1
R z
-
y(3x2 -y2)
E'
2
-1
0
2
-1
0
(x, y)
(x2 -y2 , xy)
(xz2 , yz2 ) [x(x2 +y2), y(x2 +y2)]
A'' 1
1
1
1
-1
-1
-1
-
-
-
A'' 2
1
1
-1
-1
-1
1
z
-
z3 , z(x2 +y2 )
E''
2
-1
0
-2
1
0
(R x , R y )
(xz, yz)
[xyz, z(x2 -y2)]