\b[A periodic crystal cannot have a fivefold crystallographic <rotation> axis.] The <crystallographic restriction theorem> permits <rotation> orders $1,2,3,4,6$ for a periodic <Bravais lattice>. A $72^\circ$ <rotation> cannot preserve such a lattice. This restriction concerns exact <symmetry> of the infinite <crystal structure>; an isolated finite cluster with fivefold <symmetry> is a different object.

Solution

Past exam of the materials science course of the University of Cambridge / 2022 / Paper 1 / 1 / a / i / Solution

 Solution (source code)