On the Volume Density Spectrum of Fully Augmented Links

For a hyperbolic fully augmented link in $S^3$, its \emph{FAL volume density} is the ratio of its volume to the number of augmentations. We show that the set of FAL volume densities is dense in $[2\text{voct},10\text{vtet})$, but discrete in $[\text{voct},2\text{voct})$.