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: x = a cos u sin v y = a sin u sin v z = a ( cos v + ln tan v 2 ) + b u {\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.