How many symmetry elements are there for a cubic structure or a crystal ?

Explanation

There are 3 types of symmetry elements. They are : (a) centre of symmetry, (b) axis of symmetry and (c) plane of symmetry. A cube has 1 centre of symmetry. A cube has 3 axis of four fold symmetry, 4 axis of three fold symmetry and 6 axis of two fold symmetry. A cube has 3 rectangular planes of symmetry and 6 diagonal planes of symmetry. The total number of symmetry elements of a cube = 1 + (3 + 4 + 6) + (3 + 6) = 23.