Plücker's conoid is a well-known ruled surface. As with the catenoid, another ruled surface, Plücker's conoid must be reparameterized to see the rulings:
Note that the apparent gap in the center of the surface is an artifact of the plotting, and not a feature of the surface. The rulings are the horizontal lines that pass though the z axis. A more general form of Plücker's conoid is parameterized below, with n folds instead of just two (second equations).
The non-polar parameterization of Plücker's conoid is:
Or, in polar coordinates,
where n is the number of folds in the surface. The second surface plotted above is the case n = 2.