2.7.2.2: Groups of Low and High Symmetry
- Page ID
- 294096
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Low Symmetry Point Groups
Low symmetry point groups include the C1, Cs, and Ci groups
Group | Description | Example |
---|---|---|
C1 | only the identity operation (E) | CHFClBr |
Cs | only the identity operation (E) and one mirror plane | C2H2ClBr |
Ci | only the identity operation (E) and a center of inversion (i) | C2H2Cl2Br |
High Symmetry Point Groups
High symmetry point groups include the Td, Oh, Ih, C∞v, and D∞h groups. The table below describes their characteristic symmetry operations. The full set of symmetry operations included in the point group is described in the corresponding character table.
Group | Description | Example |
---|---|---|
C∞v | linear molecule with an infinite number of rotation axes and vertical mirror planes (σv) | HBr |
D∞h | linear molecule with an infinite number of rotation axes, vertical mirror planes (σv), perpendicular C2 axes, a horizontal mirror plane (σh), and an inversion center (i) | CO2 |
Td | typically have tetrahedral geometry, with 4 C4 axes, 3 C2 axes, 3 S4 axes, and 6 dihedral mirror planes (σd) | CH4 |
Oh | typically have octahedral geometry, with 3 C4 axes, 4 C3 axes, and an inversion center (i) as characteristic symmetry operations | SF6 |
Ih | typically have an icosahedral structure, with 6 C5 axes as characteristic symmetry operations | B12H122- |