Is the cross polytope the hardest symmetric convex body to approximate by a zonoid? A zonoid is a limit of shapes made by adding line segments. The question asks how much a body must be enlarged to fit such an enclosure between the body and its enlarged copy. This candidate gives a counterexample in six dimensions. Start with the twelve coordinate vertices, four units along each positive and negative axis. Add the point with coordinates one, one, one, one, two, two, and its negative. The resulting fourteen vertex body has an exact enclosure factor of one hundred and twenty two divided by sixty five. That exceeds the cross polytope benchmark of fifteen eighths by one five hundred and twentieth. The proof has two parts. Sixty four rational signed sum identities give a lower bound valid for every generator direction. A support function argument extends that bound to every zonoid. A matching upper certificate supplies a zonotope with fifty three generators. Exact arithmetic checks all vertex representations and all thirty five facet pairs. A second check describes the polar body as a clipped cube and verifies all seventy polar vertices. Floating point optimization helped discover the witnesses, but is not needed to replay the final certificates. This does not identify the worst body in six dimensions, the smallest dimension with a counterexample, or a unique optimal enclosure. It is an unrefereed Evidence Press candidate, not a formally verified or externally peer reviewed theorem. No historical priority claim is made. The paper, exact witnesses and replay code are linked. This briefing uses an OpenAI synthetic voice and adds no mathematical evidence.