Abstract 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 n = 7, 8 n = 7, 8 and derive corresponding algebraic characterisations in terms of bracket polynomials, as well as describing a construction to produce a Poncelet 2 n -gon from a starting Poncelet n -gon.
Berman et al. (Sat,) studied this question.