Nonconic perimeter-centroid conjecture for polar polygons of bicentric images

Let $\cal{B}'$ be the conic-inscribed polar image of a generic bicentric family of $N$-gons, and let $\cal{P}'$ be the conic to which $\cal{B}'$ is inscribed. Nonconic perimeter-centroid conjecture. Over the polar polygons of $\cal{B}'$ with respect to $\cal{P}'$, the locus of the perimeter centroid is never a conic. This is presented as a further experimental generalization and is not resolved in the supplied text.