  A quadrisecant of a knot is a straight line intersecting the knot at four
points. If a knot has finitely many quadrisecants, one can replace each subarc
between two adjacent secant points by the line segment between them to get the
quadrisecant approximation of the original knot. It was conjectured that the
quadrisecant approximation is always a knot with the same knot type as the
original knot. We show that every knot type contains two knots, the
quadrisecant approximation of one knot has self intersections while the
quadrisecant approximation of the other knot is a knot with different knot
type.

Geometric Topology