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Low Symmetry Point Groups
Low symmetry point groups include the C1, Cs, and Ci groups
|only the identity operation (E)
|only the identity operation (E) and one mirror plane
|only the identity operation (E) and a center of inversion (i)
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.
|linear molecule with an infinite number of rotation axes and vertical mirror planes (σv)
|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)
|typically have tetrahedral geometry, with 4 C4 axes, 3 C2 axes, 3 S4 axes, and 6 dihedral mirror planes (σd)
|typically have octahedral geometry, with 3 C4 axes, 4 C3 axes, and an inversion center (i) as characteristic symmetry operations
|typically have an icosahedral structure, with 6 C5 axes as characteristic symmetry operations