In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. (copied from https://en.wikipedia.org/wiki/Poncelet%27s_closure_theorem)
In this visualization you can freely select the starting point of a potential polygon on an ellipse check if it forms a closed polygon. It also displays the functions of Caylyes closure conditions, that allow to find a configuration with a specific number of vertices.