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By gluing together the sides of eight copies of an all-right angledhyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds withEuler characteristic -1 are constructed. They are the first known examples oforientable hyperbolic 6-manifolds having the smallest possible volume.

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