Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

A general method of constructing families of cyclic polynomials over $\mathbb{Q}$ with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations. Using this, we obtain explicit multi-parametric families of cyclic polynomials over $\mathbb{Q}$ of degree $3\le e\le 7$. We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.