Steininger and Yurkevich's negative Rupert conjecture for three Archimedean solids

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A compact convex set S⊆R3S\subseteq\mathbb{R}^3 is Rupert if a second identical copy can pass straight through a hole in the interior of the first with rescaling factor μS>1\mu_S>1. Steininger and Yurkevich's conjecture. The rhombicosidodecahedron, snub dodecahedron, and snub cube are not Rupert. The paper motivates this negative conjecture by high-precision computational searches that did not find Rupert passages for these three Archimedean solids; failure to find such passages does not establish non-Rupertness.

References

Primary source

Raj Gosain and Benjamin Grimmer, “Some New Insights from Highly Optimized Polyhedral Passages”, arXiv:2509.08190 (2025).

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