The Beraha number $B_{10}$ is a chromatic root

This note exhibits graphs whose chromatic polynomials have the Beraha number $B_{10}=(5+\sqrt{5})\mathrm{/}2$ as a root. It was previously known that no other non-integer Beraha number is a chromatic root, and so these examples complete the determination of precisely which Beraha numbers can be chromatic roots.