Left: Steiner's Roman Surface
"Classical example of an important geometric form in the development of algebraic geometry as one of the important branches of geometry and mathematics in general. This surface was discovered by Steiner during a journey to Rome, Italy, and is known as Steiner's Roman Surface."
Right: Steiner's Cross-cap Surface
"Quartic with a double line. There are 2 pinch-points. Every plane through the double line cuts the surface in a circle. This surface is the locus of the circles of curvature of all normal sections at a point of a given surface."