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Dual of Ruperthedron is locally Rupert

Prove that the dual of the Ruperthedron is locally Rupert (for an appropriate definition of dual), thereby confirming the authors’ belief and clarifying the duality behavior with respect to local Rupert property.

References

We note that the Ruperthedron is a natural candidate for disproving Conjecture 2 in [Scott2022]: We believe that its dual (for any reasonable definition of this term) is locally Rupert but leave the proof for future work.

A convex polyhedron without Rupert's property (Steininger et al., 25 Aug 2025) in Section 8, Rupert but not locally Rupert