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$$\varphi(u,v)=\left( \begin{array}{c} v\cos\alpha\cos u - \sin u\\ v\cos\alpha\sin u + \cos u\\ v\sin\alpha \end{array} \right)\qquad \begin{array}{l} u\in(0,2\pi)\\ v\in\mathbb{R} \end{array} $$