Abstract. The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0, voct]. We construct sequences of alternating knots whose volume and determinant densities both converge to any x ∈ [0, voct]. We also investigate the distributions of volume and determinant densities for hyperbolic rational links, and establish upper bounds and density results for these invariants.
Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multicrossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L given its multicrossing projection. These bounds are realized by three closely related infinite tiling weaves.
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