1. Special Group Elements
Structure
linear
Yes
Yes
D∞h i
Linear
C∞v No
Linear or
low symmetry
Yes σ
Yes
Special Group Elements Cs
Yes No Ci i
Single
Element No C1
Yes Ih
highly
symmetric
(octahedral,
tetrahedral,
icosahedral)
Sure? More
than one Cn
axis of C3
or higher?
6C5
Yes i
Icosahedral
Yes
Yes I No No
Yes Oh
3C4
Yes i
Octahedral O No No
High Symmetry
Elements No
3s4
Yes Td No
Yes Th i
Tetrahedral No T σh
Dnh
C2  Cn
Yes
Yes
Yes
Normal
symmetry
Yes
nσd
Dnd
Dihedral No No Dn
Normal
Symmetry
Elements
(most common) σh
Yes
Cnh No
nσv
Yes
Cnv
Single axis No
S2n
Yes
S2n No Cn