A trivial knot whose spanning disks have exponential size

If a closed curve in space is a trivial knot (intuitively, one can untie it without cutting) then it is the boundary of some disk with no self-intersections. In this paper we investigate the minimum number of faces of a polyhedral spanning disk of a polygonal knot with <italic>n</italic> segments. We exhibit a knot whose minimal spanning disk has exp(<italic>cn</italic>) faces, for some positive constant <italic>c</italic>.