The surface shown in "TriplePoint Twist" is one from a series of surfaces described by David Mond and Washington Marar in [MM], where they analyze a number of germs of singularities of surfaces. This particular example is a ruled surface given by the equations
(x,y,z) = (u, v^{3} + cv, uv + v^{5} + cv^{3}) where c is a parameter that can be varied. For values of c greater than 0, the surface has no selfintersection, but for values of c less than 0, a TriplePoint and two pinch points appear. For the image shown in the exhibit,
c = 1 , but an MPEG movie is available showing a series of different values of c as it varies from 1 to 1. For each fixed value of u, allowing v to vary produces a planar curve in the planex = u . The rulings for the surfaces are the straight lines produced when v is held fixed and u is allowed to vary. One of the MPEG movies shows the surface being swept out by these ruling lines.

