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Rhombicosidodecahedron non-Rupert conjecture

Prove that the Rhombicosidodecahedron does not have Rupert’s property, thereby resolving the conjecture that this specific Archimedean solid fails to be Rupert.

References

In [Conjecture 2]{StYu23} we conjectured that the Rhombicosidodecahedron (RID in short) does not have Rupert's property. We still believe this conjecture, however the methods of this paper do not suffice to prove it.

— A convex polyhedron without Rupert's property (Steininger et al., 25 Aug 2025) in Section 9.1, Origin of the Noperthedron