Plücker's Conoid 

Introduction:Plücker's conoid is a wellknown 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). Definition:The nonpolar 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. Properties:
