Right-angled Coxeter polytopes, hyperbolic 6-manifolds, and a problem of Siegel

Brent Everitt, John G. Ratcliffe, Steven T. Tschantz

By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constr…