Sextic reciprocal monogenic dihedral polynomials

Let $D_n denote the dihedral group of order 2n. We find infinite D_6 -families and an infinite D_3 -family of monic irreducible reciprocal sixth-degree polynomials f(x)\in \mathbb {Z}[x] , such that \{1,\theta ,\theta ^2,\theta ^3,\theta ^4,\theta ^5\} is a basis for the ring of integers of L=\mathbb {Q}(\theta ) , where f(\theta...