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Banibrata majumder Best Answer
There is only available symmetry of 1,2,3,4 & 6- fold symmetry operations as any kind of 5 of more than 6 - fold symmetry is not able to completely cover a three dimensional space as a whole. 5-fold symmetry elements are not able to represent the whole space at all. Thus, there is no 5-fold symmetry element available for crystal analysis. The length, edges of principal axes, and angle between unit cells are all lattice constants. We can't pack objects like pentagons or octagons such that they fill up space entirely and that that's one reason there is no 5-fold or 8-fold rotational axis.