Poncelet's Porism and (n4)-configurations:

The collection of animations you find here refers to a series of articles jointly written by Leah Wrenn Berman, Gábor Gévay, Jürgen Richter-Gebert and Serge Tabachnikov about surprising connections of Poncelet's Porism on polygons and conics and $(n_4)$-configurations. We show that a large class of configurations exhibit a non-trivial movement via Poncelets Theorem. We provide constructions, algebraic characterisations and a general theorem that ensures movability for a wide range of (n4)-configurations.

These animations refer to:
"When Grünbaum meets Poncelet -- Infinite Classes of Movable n4 Configurations"
"Explicit Constructions for Poncelet Polygons"

Interactive pages

Constructions of Poncelet Polygons

construction of 7-gon construction of 8-gon

Basic facts on Poncelet's Porism

Poncelet's Porism elliptical billiards

The main construction

main construction configurator

Long Poncelet chains

constructing an $\infty$-gon $\infty$-gon on a conic

Relation to incircle nets

incircles of Poncelet grid from incircles to $(n_4)$

Advanced examples

a $(120_6)$-configuration a $(21_7)$ of conics