  In [6], Kellerhals and Perren conjectured that the growth rates of the
reflection groups given by hyperbolic Coxeter polyhedra are always Perron
numbers. We prove that this conjecture is always true for the case of ideal
Coxeter polyhedra in $\mathbb{H}^3$. We also find out the ideal Coxeter
polyhedron in $\mathbb{H}^3$ with the smallest growth rate. Finally, we show
that there are correlations between the volumes and the growth rates of ideal
Coxeter polyhedra in $\mathbb{H}^3$ in many cases.
