  The $\textit{volume density}$ 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 $v_8$, where $v_8$ is the volume of the ideal hyperbolic
octahedron. We show that the set of volume densities is dense in $[0,v_8]$. The
$\textit{determinant density}$ of a link $K$ is $[2 \pi \log \det(K)]/c(K)$. We
prove that the closure of the set of determinant densities contains the set
$[0, v_8]$.
