  Given a planar pentagon, construct two new pentagons: the vertices of the
first one are the intersection points of the diagonals of the original
pentagon, and the vertices of the second one are the tangency points of the
conic inscribed in the original pentagon. E. Kasner theorem, published in 1928,
asserts that these two operations on pentagons commute. We extend Kasner's
result to Poncelet polygons, that is, the polygons inscribed into a conic and
circumscribed about a conic.
