On the Davis hyperbolic 4-manifold

We algebraically characterize the Davis hyperbolic 4-manifold as the orbit space of the unique torsion-free normal subgroup of index 14,400 of the (5,3,3,5) Coxeter simplex reflection group acting on hyperbolic 4-space. We determine the homology, injectivity radius, and the group of isometries of the Davis manifold. We show that the Davis manifold is a spin manifold.