The Quartic paraboloid is similar to a paraboloid, but has a squarer shape. There are creases along the X, Y and Z axes where the pads meet. It is a model of the projective plane. The Strophid is like an infinite plane with a bulb sticking out of it.
Larger values give larger bulbs.
Negative values give a bulb on the other side of the plane. When zero, the bulb is like a sphere that just touches the plane. When positive, there is a crossover point. When negative the bulb simply bulges out of the plane like a pimple. Higher values make the top end of the bulb fatter.