TwoFamilies(Parabola)::usage=" Poncelet's porism says that whenever a polygon is inscribed in a conical and circumscribes another, the polygon must be part of an infinite family of polygons that are all inscribed and circumscribe the same two conicals. References: Wolfram MathWorld: Poncelet's Porism; YouTube: Exploring the Dynamic Geometry and Conservations of the Steiner-Soddy and Harmonic Poncelet Porism, Dan Reznik; Personal. ";
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The circumference that passes through the tangential points of the circles of the Steiner chain is inscribed in the family of polygons 1 (in orange) that have their vertices on a parabola. The family of polygons 2 (in dark green) is inscribed in this circle, its vertices are the tangent points of the circles of the Steiner chain.