On the growth rates of cofinite 3-dimensional hyperbolic Coxeter groups whose dihedral angles are of the form $\frac{\pi }{m}$ for $m=2,3,4,5,6$

Abstract

We study arithmetic properties of the growth rates of cofinite 3-dimensional hyperbolic Coxeter groups whose dihedral angles are of the form $\frac{\pi }{m}$ for $m=2,3,4,5,6$ and show that the growth rates are always Perron numbers.