Dini's surface

In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere. It is named after Ulisse Dini and described by the following parametric equations:
 * $$\begin{align}

x&=a \cos u \sin v \\ y&=a \sin u \sin v \\ z&=a \left(\cos v +\ln \tan \frac{v}{2} \right) + bu \end{align}$$ Another description is a generalized helicoid constructed from the tractrix.