Rhombicosidodecahedron non-Rupert conjecture

Prove that the Rhombicosidodecahedron (RID) does not have Rupert’s property. Establishing this would resolve a standing conjecture about the Rupert status of the RID.

Background

The authors previously conjectured that the Rhombicosidodecahedron fails to have Rupert’s property, but their current techniques do not resolve this case. They indicate that certain local configurations prevent a straightforward application of their local theorem, leaving the conjecture unproven.

Confirming the conjecture would extend the negative results beyond the Noperthedron, clarifying the boundary of Rupert’s property among well-known highly symmetric polyhedra.