Properties of Point Mass Lenses On A Regular Polygon and The Problem of Maximum Number of Images

We study the critical curves, caustics, and multiple imaging due to one of the simplest many-body gravitational lens configurations: equal-mass point masses on the vertices of a regular polygon. Some examples of the critical curves and caustics are also displayed. We pose the problem of determining the maximum number of lensed images due to regular-polygon and general point mass configurations. Our numerical simulations suggest a maximum that is linear, rather than quadratic, in the number of point masses.