This is a depiction of the nodal cubic curve or singular cubic curve. (See e.g. http://www.math.purdue.edu/~dvb/graph/nodal.html or http://en.wikipedia.org/wiki/Cubic_plane_curve) Typically it's completed from \R^2 = \C to \CP^1 but I've lifted it to the double cover S^2. The latitudes of this S^2 in the model together with the radially extruded curve highlight its geometry. This was created with Drew Armstrong.