Symmetry operations are movements or actions that leave the molecule apparently unchanged.

Symmetry elements are the points, lines, or planes in space about which the symmetry operation takes place

Every object belongs to a characteristic group called the ‘point group’ that describes/contains all the symmetry operations/elements of that object.

Performing a symmetry operation leaves the molecule/object apparently unmoved!

An octahedron has the same symmetry properties of a cube

A tetrahedron contains a subset of the symmetry properties of a cube

Example of an Improper-Rotation Axis

Point Group Flow Chart (or Decision Tree)