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 \(f(\theta )=0\).

中文翻译：

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互惠性单基因二面体多项式

令\（D_n \）表示2 n阶二面体组。我们在\ mathbb {Z} [x] \）中找到无限的（（D_6 \）-族和无限的（（D_3 \）-）单项不可约的倒数六次多项式\（f（x）\），使得\ （\ {1，\ theta，\ theta ^ 2，\ theta ^ 3，\ theta ^ 4，\ theta ^ 5 \} \）是\（L = \ mathbb {Q}（ \ theta）\），其中\（f（\ theta = 0 = 0））。