The vertices of polyhedral protein capsules are spanned by multiple capsule-forming protein subunits, thus enclosing more volume and larger cargoes than if single proteins connect vertices directly. Application of protein cage design principles to synthetic analogues would allow a given ligand to enclose a greater volume. Here we report the self-assembly of a simple tetramine subcomponent into a tetrahedral metal-organic capsule, with each face of the capsule composed of three ligand panels. The edges of the capsule are 31.8 Å in length — double the distance that can be spanned by a single subcomponent. The self-assembly rules followed by this system are programmed into the tetramine — it twists out of planarity in its lowest-energy configuration, thus favouring the large capsule over a simpler cube-like architecture. Unlike other large metal-organic capsules, the cavity of this new capsule is enclosed and the structure was observed to bind large dianionic guests.