The answer is simple. Inorder to represent the permutation of indices of the form consistent, MB indices are used in hcp. that is... in hcp planes of the form {100} do not include the plane of the type (10-10) ie (100) does not include (1-10) which belongs to the same set of planes which are called prismatic planes.. Hence a third axis is chosen so that the planes of the form {10-10} include the following planes (10-10),(1-100),(-1100),(0-110),(01-10) etc. So choosing the four index systems has made the set of planes belong to that particular form avoiding confusion thereby making permuatation of indices and symmetry more obvious
In Choosing four index system actually one of the axes in the basal plane is redundant by making it dependent on the other two ensuring that the planes belong to a particular form. This is better explained in a book of crystal chemistry by Relva C. Buchanan, Taeun Park.
Please contribute to this article as well if you have more conclusive, concrete solid answer
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