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For each natural number n >= 4, we determine the unique lowest volumehyperbolic 3-orbifold whose torsion orders are bounded below by n. This lowestvolume orbifold has base space the 3-sphere and singular locus the figure-8knot, marked n. We apply this result to give sharp lower bounds on the volumeof a hyperbolic manifold in terms of the order of elements in its symmetrygroup.

The lowest volume 3-orbifolds with high torsion