Explicit Constructions for Poncelet Polygons

We study the geometric structure of Poncelet n-gons from a projective point of view. In particular we present explicit constructions of Poncelet n-gons for certain n and derive algebraic characterisations in terms of bracket polynomials. Via the connections of Poncelet polygons and (N₄)-configurations, the results of this article can be used to construct a large class of specific movable (N₄)-configurations, the trivial celestial 4-configurations, which up to this point were all thought to be rigid and to require regular polygons for their construction.