Commonly, materials are classified as either electrical conductors or insulators. The theoretical discovery of topological insulators has fundamentally challenged this dichotomy. In a topological insulator, the spin-orbit interaction generates a non-trivial topology of the electronic band structure dictating that its bulk is perfectly insulating, whereas its surface is fully conducting. The first topological insulator candidate material put forward - graphene - is of limited practical use because its weak spin-orbit interactions produce a bandgap of ∼ 0.01 K. Recent reexaminations of Bi ₂Se₃ and Bi₂Te₃, however, have firmly categorized these materials as strong three-dimensional topological insulators. We have synthesized the first bulk material belonging to an entirely different, weak, topological class, built from stacks of two-dimensional topological insulators: Bi₁₄Rh₃I₉. Its Bi-Rh sheets are graphene analogues, but with a honeycomb net composed of RhBi 8 cubes rather than carbon atoms. The strong bismuth-related spin-orbit interaction renders each graphene-like layer a topological insulator with a 2,400 K bandgap.