Maeder's Owl Minimal Surface

A Minimal Surface which resembles a Cross-Cap. It is given by the polar equations

$$x = 1$$ (1)

$$y = \sqrt{z}$$ (2)

$$z = z,$$ (3)

or the parametric equations

$$x = r\cos\theta-{\textstyle{1\over 2}}r^2\cos(2\theta)$$ (4)

$$y = -r\sin\theta-{\textstyle{1\over 2}}r^2\sin(2\theta),$$ (5)

$$z = {\textstyle{4\over 3}} r^{3/2}\cos({\textstyle{3\over 2}}\theta).$$ (6)

See also Cross-Cap, Minimal Surface

References

Maeder, R. Programming in Mathematica, 3rd ed. Reading, MA: Addison-Wesley, pp. 29-30, 1997.