The spectra of volume and determinant densities of links

The volume density of a hyperbolic link K is defined to be the ratio of the hyperbolic volume of K to the crossing number of K  . We show that there are sequences of non-alternating links with volume density approaching voctvoct, where voctvoct is the volume of the ideal hyperbolic octahedron. We show that the set of volume densities is dense in [0,voct][0,voct]. The determinant density of a link K   is 2πlog⁡det⁡(K)/c(K)2πlog⁡det⁡(K)/c(K). We prove that the closure of the set of determinant densities contains the set [0,voct][0,voct].