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The Volume Spectrum of Hyperbolic 4-Manifolds

The Volume Spectrum of Hyperbolic 4-Manifolds

We construct complete, open, hyperbolic 4-manifolds of smallest volume by gluing together the sides of a regular ideal 24-cell in hyperbolic 4-space. We also show that the volume spectrum of hyperbolic 4-manifolds is the set of all positive integral multiples of 47π2/3.