21 points and 21 lines. Four lines passing through each point and 4 points on each line: Grünbaum and Rigby’s configuration 21_4 was discovered in 1990 and since then always drawn in exactly the same way – three nested regular heptagons adjusted carefully to satisfy the incidence relations. It turns out that this configuration (as well as many of its relatives) is more flexible than it was assumed for a long time. There is a recently discovered subtle relation between celestical n4 configurations and the classical theorem of Poncelet from 1822 that allows to transfer the flexibility of Poncelet's configurations to a non-rigidity statement for n4 configurations. The proof turns out to be related to regular arrangements of circles, the geometry of elliptical billiards, and discrete differential geometry. Moreover in the talk explicit geometric constructions for specific values of n that allow to control the full motional freedom as well as invariant theoretic algebraic characterizations will be given. The talk will be illustrated by various interactive geometric visualisations and images.