Lichtenfels Surface

A Minimal Surface given by the parametric equation

$$x = \Re\left[{\sqrt{2}\cos({\textstyle{1\over 3}}\zeta)\sqrt{\cos({\textstyle{2\over 3}}\zeta)}\,}\right]$$

$$y = \Re\left[{-\sqrt{2}\cos({\textstyle{1\over 3}}\zeta)\sqrt{\cos({\textstyle{2\over 3}}\zeta)}\,}\right]$$

$$z = \Re\left[{-{\textstyle{1\over 3}}\sqrt{2}\,i\int_0^t {d\zeta\over \sqrt{\cos({\textstyle{2\over 3}}\zeta)}}}\right].$$

References

do Carmo, M. P. ``The Helicoid.'' §3.5F in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, p. 47, 1986.

Lichtenfels, O. von. ``Notiz über eine transcendente Minimalfläche.'' Sitzungsber. Kaiserl. Akad. Wiss. Wien 94, 41-54, 1889.