  A quadruple crossing is a crossing in a projection of a knot or link that has
four strands of the knot passing straight through it. A quadruple crossing
projection is a projection such that all of the crossings are quadruple
crossings. In a previous paper, it was proved that every knot and link has a
quadruple crossing projection and hence, every knot has a minimal quadruple
crossing number. In this paper, we investigate quadruple crossing number, and
in particular, use the span of the bracket polynomial to determine quadruple
crossing number for a variety of knots and links.
