In this talk, we introduce point-ellipse configurations and point-conic configurations. We present some of their basic properties and describe two interesting families of balanced point-conic 6-configurations. The construction of the first family is based on Carnot’s theorem, whilst the construction of the second family is based on the Cartesian product of two regular polygons. Finally, we investigate a point-ellipse configuration based on the regular 24-cell.

This is joint work with Gábor Gévay, Jurij Kovič and Tomaž Pisanski.