This paper is devoted to the proof of existence of q-periodic alternating projections of prime alternating q-periodic knots. The main tool is the Menasco-Thistlethwaite's Flyping Theorem.

Let K be an oriented prime alternating knot that is q-periodic with $q\ge 3$, i.e. that admits a rotation of order q as a symmetry. Then K has an alternating projection $\mathrm{\Pi }(K)$ such that the rotational symmetry of K is visualized as a rotation of the projection sphere leaving $\mathrm{\Pi }(K)$ invariant.

As an application, we obtain that the crossing number of a q-periodic alternating knot with $q\ge 3$ is a multiple of q. Furthermore we give an elementary proof that the knot $12a_{634}$ is not 3-periodic; our proof does not depend on computer calculations as in [11].

本文致力于证明质数交替q-周期结的q-周期交替投影的存在性。主要工具是 Menasco-Thistlethwaite 的飞行定理。

设K是一个有向质数交替结，它是q周期的$q\ge 3$，即允许q阶旋转作为对称性。那么K有一个交替投影$\mathrm{\Pi }(钾)$使得K的旋转对称性可视化为投影球体的旋转离开$\mathrm{\Pi }(钾)$ 不变的。

作为一个应用，我们得到一个q周期交替结的交叉数与$q\ge 3$是q的倍数。此外，我们给出了一个基本的证明，即结$12{\mathrm{一种}}_{634}$不是 3-周期的；我们的证明不依赖于 [11] 中的计算机计算。