Axes of rotation Cn

A molecule has an axis of rotation of degree n, or an n—fold rotation axis, if rotation by th of a full turn is a covering operation. If n = 2, the rotation is by half a turn, or 180°, as in the case of the C2 axis of the water molecule. The symbol denotes an n—fold axis. 

Axes of rotation are among the most common of molecular symmetry operations. A onefold axis is a rotation by a full turn, equivalent to the identity. A twofold rotation axis, as in the example of the water molecule, is sometimes called a dyad. Cyclopropane has a threefold axis perpendicular to the plane containing the carbon atoms it also has three twofold axes. Can you visualize them  

A molecule has a plane of symmetry, or mirror plane, if reflection of all atoms in the plane is a covering operation. 

Any planar molecule has mirror symmetry, because reflection in the molecular plane leaves the positions of all atoms unaltered. For planar molecules, mirror reflection in the molecular plane is equal to the identity. A molecule may have several mirror planes recall that the water molecule has two - it is symmetric both with respect to the molecular plane and with respect to a plane perpendicular to the molecule. 

Mirror planes are denoted by the Greek letter a. Mirror planes in a molecule that has an axis of rotation are further classified according to the relative orientation of the axis and the mirror plane. Because it is usual to draw molecules with the principal rotation axis vertical, a mirror plane containing the principal rotation axis is called a vertical mirror and denoted. A mirror plane perpendicular to the rotation axis is called a horizontal mirror and denoted Oh- 

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