AbstractIfnis divisible by at least three distinct primes, the dihedral groupDncan be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation ofDnfor several families ofnand for all admissiblen<120. All these graphs are trivalent, bipartite, Hamiltonian, of girth 6, and are regular representations of their groups. For eachn, the isomorphism classes are determined and the graphs are described by a simple code.