From incircles to $(n_4)$-configuration

Move the big white point to rotate. Click buttons to show different parts of the configuration

If a Poncelet polygon comes from two confocal conics one can directly construct an $(n_4)$-configuration from the various incircles of cells and compound cells of the Poncelet grid.

This animation illustrates the process

• lines: the lines tangent to the inner Poncelet conic.
• incircles: various incircles, the blue circles belong to compond cells.
• centers: the centers of the incircles.
• config: the resulting $(n_4)$-configuration.