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

A motif can have fivefold symmetry. For example, repeat an identically oriented regular pentagonal molecular motif at every point of a square translation lattice. Each isolated motif has fivefold rotational symmetry, while the crystal structure as a whole does not: rotating about one motif fails to map the other motif centres onto lattice points. The symmetry of an atomic basis of a crystal need not be a symmetry of its Bravais lattice.