Dini's surface

In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere.¹ It is named after Ulisse Dini² and described by the following parametric equations:³

${\displaystyle {\begin{aligned}x&=a\cos u\sin v\\y&=a\sin u\sin v\\z&=a\left(\cos v+\ln \tan {\frac {v}{2}}\right)+bu\end{aligned}}}$

Another description is a generalized helicoid constructed from the tractrix.⁴