This paper describes the Cheng-Pleijel points of a closed convex body in Euclidean space. An integrability condition depending only on the curvature and support function is derived which describe the points completely. Reference: Geom. Dedicata,44, 1992,pp. 139-145.

For the kids, explore the Cheng-Pleijel points of a quadrangle with this java application! Requires a browser with beta api support such as Netscape 2.0 or better. Depending on the type of machine, it may take a while to load. Here is the text of the applet.