  Four packings of hyperbolic 3-space are known to yield the optimal packing
density of $0.85328\dots$. They are realized in the regular tetrahedral and
cubic Coxeter honeycombs with Schl\"afli symbols $\{3,3,6 \}$ and $\{4,3,6\}$.
These honeycombs are totally asymptotic, and the packings consist of horoballs
(of different types) centered at the ideal vertices. We describe a method to
visualize regular horoball packings of extended hyperbolic 3-space
$\bar{\mathbb{H}}^3$ using the Beltrami-Klein model and the Coxeter group of
the packing. We produce the first known images of these four optimal horoball
packings.
