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Chem 104A, UC, Berkeley
Groups generated by an Sn axis: Snn odd Cnhn even: Sn
iCS 2
H
HCl
Cl
F
FhC3
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
4
342
244 },,,{
S
SCSSE
1,3,5,7-tetrafluorocyclooctatetraene
F
F
F
F
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
Dihedral groups:Groups with a Cn axis plus n perpendicular C2 axes: Dn
C2H6 partly rotated (not staggered, not eclipsed).
},,,,,{ ''2
'22
2333 CCCCCED
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
Other example:
32422 )( NHHCNHCo
22422 )( NHHCNHPt
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Chem 104A, UC, Berkeley
Chem 104A, UC, BerkeleyGroups with a Cn axis, n C2 axes and a h plane: Dnh
Example: Eclipsed Conformation of Hydrazine, N2H4
},,,),(),(),(,{ 2222 xzyzxyh ixCyCzCED
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Chem 104A, UC, Berkeley
D3h: BF3
}'',',,,,,'',',,,,{ 533222
2333 vvvhh SSCCCCCED
Chem 104A, UC, Berkeley
D4h: PtCl4
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Chem 104A, UC, Berkeley
,....},,,.........,.....,,{
,
2
22:
SiCCE
BeFHD
hv
h
n-gonal prism
Chem 104A, UC, Berkeley
n-gonal prism
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Chem 104A, UC, Berkeley
Groups with a Cn axis, n C2 axes, and n d planes: Dnd
Symmetry Elements for D3d Point Group (A2X6)
C2H6 staggered.
}'',',,,,,'',',,,,{ 566222
2333 dddd SSiCCCCCED
d: dihedral reflection planes (bisects v or C2)
Chem 104A, UC, Berkeley
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Chem 104A, UC, Berkeley
}',,'',',,,,{ 2234422 ddd CCSSCED
Allene
C
C
C
staggered regular polygons (n-gonal antiprism)
Chem 104A, UC, Berkeley
B2Cl4
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Chem 104A, UC, Berkeley
Chem 104A, UC, Berkeley
Groups with very high symmetry: multiple high-fold rotation axes
The platonic solids: polyhedra constructed from regular polygons with all vertices and edges equivalent: 5 possibilities only.
icosahedron