Take a flat, flexible ring, such as a rubber washer. It has an inner radius for its inner circle, and an outer radius for its outer circle. Fold it so that the inner circle of the washer joins up with itself in a half-circle, and the outer circle remains loose. Then pinch the inner circle shut so that it becomes a line segment, still leaving the outer circle loose.
Is there a name for the resulting saddle-like surface?
A version of this surface can be plotted in polar coordinates as $f(r, \theta) = sin(2 \theta)$.
A 3d plot on sage cell (click and drag to move the figure): here