TUD Organische ChemieImmelTutorialsSymmetrySymmetry and Shape of ObjectsView or Print this frame onlyView or Print (this frame only)

Top of Page Molecular Structures of Organic Compounds - Symmetry and Shape of Objects
Symmetry and Shape of Objects:

The table below provides an overview on the shapes of objects belonging to various point groups. The group to which a molecule belongs may often be determined from these shapes without going through the entire formal procedure of determining all symmetry elements. For the more detailed and accurate procedure of point group determination see the flowchart in the 'Point Group Separation Procedure' section.

Symmetry and Point Groups
Symmetry Elements of a 3D-Object
Top of Page The Shape of Objects of Some Point Groups
The Shape of Objects

Top of Page Three-dimensional Shape of Objects
An alternative view on the various three-dimensional shapes belonging to the different point groups is given by the table below (chiral point groups are marked by bold-face point group symbols):

General*   Point Groups and Shapes of Three-dimensional Objects*
   
n = 1
n = 2
n = 3
n = 4
n = 5
n = 6
n = ∞
Cn  
Three-dimensional Shape of Point Group C1
Three-dimensional Shape of Point Group C2
Three-dimensional Shape of Point Group C3
Three-dimensional Shape of Point Group C4
Three-dimensional Shape of Point Group C5
Three-dimensional Shape of Point Group C6
-
   
C1
C2
C3
C4
C5
C6
 
Cnv  
-
Three-dimensional Shape of Point Group C2v
Three-dimensional Shape of Point Group C3v
Three-dimensional Shape of Point Group C4v
Three-dimensional Shape of Point Group C5v
Three-dimensional Shape of Point Group C6v
Three-dimensional Shape of Point Group Cinfv
     
C2v
C3v
C4v
C5v
C6v
C∞v
Cnh  
Three-dimensional Shape of Point Group Cs
Three-dimensional Shape of Point Group C2h
Three-dimensional Shape of Point Group C3h
Three-dimensional Shape of Point Group C4h
Three-dimensional Shape of Point Group C5h
Three-dimensional Shape of Point Group C6h
-
   
(C1h = ) Cs
C2h
C3h
C4h
C5h
C6h
 
Dn  
-
Three-dimensional Shape of Point Group D2
Three-dimensional Shape of Point Group D3
Three-dimensional Shape of Point Group D4
Three-dimensional Shape of Point Group D5
Three-dimensional Shape of Point Group D6
-
     
D2
D3
D4
D5
D6
 
Dnh  
-
Three-dimensional Shape of Point Group D2h
Three-dimensional Shape of Point Group D3h
Three-dimensional Shape of Point Group D4h
Three-dimensional Shape of Point Group D5h
Three-dimensional Shape of Point Group D6h
Three-dimensional Shape of Point Group Dinfh
     
D2h
D3h
D4h
D5h
D6h
D∞h
Dnd  
-
Three-dimensional Shape of Point Group D2d
Three-dimensional Shape of Point Group D3d
-
-
-
-
     
D2d
D3d
       
Sn  
-
Three-dimensional Shape of Point Group Ci
-
Three-dimensional Shape of Point Group S4
-
Three-dimensional Shape of Point Group S6
-
   
(S1 = Cs)
(S2 = ) Ci
(S3 = C3h)
S4
(S5 = C5h)
S6
 
T  
Three-dimensional Shape of Point Group T
Three-dimensional Shape of Point Group Td
Three-dimensional Shape of Point Group Th
       
   
T
Td
Th
       
O  
Three-dimensional Shape of Point Group O
Three-dimensional Shape of Point Group Oh
         
   
O
Oh
         
I  
Three-dimensional Shape of Point Group I
Three-dimensional Shape of Point Group Ih
         
   
I
Ih
         
K  
Three-dimensional Shape of Point Group Kh
           
   
Kh
           
[*] Schematic plots of three-dimensional shapes belonging to the different point groups. The equator plane of all objects is marked by a pale yellow circular plane, all mirror planes are designated by transparent orange planes, axes of rotation and rotary-reflection are indicated by solid orange lines. All symmetry elements intersect in the geometrical center of each object.

For more information on other research topics, please refer to the complete list of publications and to the gallery of graphics and animations.

© Copyright PD Dr. S. Immel

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