For a nonzero vector v in R^{3}, let p_{v} denote perpendicular projection onto
the span of v. For a knot K, let b_{v} denote the number of components of the preimage of the set of local maximum values of p_{v} restricted to K. Randell, referenced below, observed that the super bridge index is bounded above by twice the polygon index.

The bridge number of K is the minimum value of b_{v} taken over all nonzero v and all knots isotopic to K.

The superbridge index is the minimum over all knots isotopic to K of the maximum of b_{v}, taken over all v.

Randell made the observation that superbridge(K) ≤ polygonnumber(K)/ 2

** References**

C. B. Jeon and G. T. Jin,
*There are only finitely many 3-superbridge knots,* Knots in Hellas '98, Vol. 2 (Delphi).
J. Knot Theory Ramifications **10** (2001), no. 2, 331--343.

C. B. Jeon and G. T. Jin, *A computation of superbridge index of knots,* (English. English summary)
Knots 2000 Korea, Vol. 1 (Yongpyong).
J. Knot Theory Ramifications **11** (2002), no. 3, 461--473.

N. H. Kuiper,
*A new knot invariant,*
Math. Ann. **278** (1987), no. 1-4, 193--209.

R. Randell, *Invariants of piecewise-linear knots,* Knot theory (Warsaw, 1995), 307--319, Banach Center Publ., **42**, Polish Acad. Sci., Warsaw, 1998.
(This is the source for the data in the table for knots with 9 or fewer crossings.)

Further information on particular knots.