Grünbaum and Rigby’s configuration 214 was discovered in 1990 and since then always drawn in exactly the same way: Three nested regular heptagons adjusted carefully such that one gets a configuration with 21 points and 21 lines with 4 points on each line and 4 lines through each point. We present recently discovered relations between ($n_4$) incidence configurations and the classical Poncelet Porism. Poncelet’s result from 1822 can be interpreted as a flexibility statement on polygons that are simultaneously inscribed into one an circumscribed around another conic. It will be demonstrated how this flexibility can be transformed to motions of ($n_4$)-configurations that result in additional degrees of freedom. The proof of this result touches various areas as diverse as geometry of billiards, regular arrangements of circles, discrete differential geometry, algebraic geometry, invariant theory and elliptic functions. We will give a brief overview how these areas come together in that context.
Moreover we provide explicit geometric constructions for specific values of $n$ that allow to control the full motional freedom and we give algebraic characterisations of the underlying Poncelet Polygons. The talk will be illustrated by various interactive geometric visualisations and images.