Question

Why a lattice with five fold symmetry not possible?

Answer 1

The symmetry of crystals. The crystallographic restriction theorem. Although objects themselves may appear to have 5-fold, 7-fold, 8-fold, or higher-fold rotation axes, these are not possible in crystals. ... The reason is that the external shape of a crystal is based on a geometric arrangement of atoms.

Answer 2

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The crystallographic restriction theorem. Although objects themselves may appear to have 5-fold, 7-fold, 8-fold, or higher-fold rotation axes, these are not possible in crystals.... The reason is that the external shape of a crystal is based on a geometric arrangement of atoms.