Knots with equal bridge index and braid index

In this paper, we are interested in BB knots, namely knots and links whose bridge index braid equal. Supported by observations from experiments, it is conjectured that possess a special geometric/physical property (and might even be characterized it): if the knot realized (closed) springy metal wire, then equilibrium state of wire an almost planar configuration multiple (overlapping) circles. provide heuristic explanation to conjecture explore plausibility numerically. We also identify among various families. For example, able all family alternating Montesinos as well some non-alternating more generally Conway algebraic knots. The identified families considered include 182 one component with crossing number up 12. Furthermore, show given [Formula: see text] grows exponentially text].