Settle the Rupert property for the three remaining Archimedean solids: rhombicosidodecahedron, snub cube, snub dodecahedron

A convex polyhedron $P$ has the *Rupert property* if a straight tunnel can be bored through $P$ through which a second congruent copy of $P$ can pass. Equivalently: there exist rotations $R_1, R_2 \in SO(3)$ and a translation $t \in \mathbb{R}^2$ such that $\pi(R_2 P) + t$ is contained in the interior of $\pi(R_1 P)$, where $\pi$ is the orthogonal projection onto a fixed plane. Ten of the thirteen Archimedean solids are proven Rupert. For the remaining three — the rhombicosidodecahedron, the snub cube, and the snub dodecahedron — the question is open. The rhombicosidodecahedron is conjectured NOT to be Rupert. Decide the Rupert property for each of the three.

Acceptance. FULLY RESOLVES (per solid; each solid is an independent deliverable): EITHER a Rupert passage certificate — explicit R_1, R_2, t (exact algebraic or interval-certified numerics) with a verification script confirming the strict containment of shadows — OR a proof of non-Rupertness (e.g., adapting the certified branch-and-bound analysis of arXiv:2508.18475), with the certificate/code public and re-runnable. ADVANCES: a rigorous reduction of the search space (e.g., certified exclusion of symmetry classes of directions), or a verified tightening of the best-known Nieuwland-type margins for these solids.