Let 
be a heptagon with seven vertices given in cyclic order inscribed in a conic.
Then the Pascal lines of the seven hexagons
obtained by omitting each vertex of 
in turn and keeping the remaining vertices in the same cyclic
order are the sides of a heptagon 
which circumscribes a conic.
Moreover, the Brianchon points of the seven hexagons obtained by omitting the sides of 
one at a time and keeping the remaining sides in the natural
cyclic order are the vertices of the original heptagon.
