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

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Abstract

By gluing together the sides of eight copies of an all-right angled hyperbolic six-dimensional polytope, two orientable hyperbolic six-manifolds with Euler characteristic −1 are constructed. They are the first known examples of orientable hyperbolic six-manifolds having the smallest possible volume.

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Everitt, B., Ratcliffe, J.G. & Tschantz, S.T. Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel. Math. Ann. 354, 871–905 (2012). https://doi.org/10.1007/s00208-011-0744-2

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