Self-assembly of multiple components into well-defined and predictable structures remains one of the foremost challenges in chemistry. Here, we report on the rational design of a supramolecular cage assembled from 20 ions of three distinct species through 72 hydrogen bonds. The cage is constructed from two kinds of hexagonal molecular tiles, a tris(guanidinium) nitrate cluster and a hexa(4-sulfonatophenyl)benzene, joined at their edges through complementary and metrically matched N-H center dot center dot center dot O-S hydrogen bonds to form a truncated octahedron, one of the Archimedean polyhedra. The truncated octahedron, with an interior volume of 2200 cubic angstroms, serves as the composite building unit of a body-centered cubic zeolite-like framework, which exhibits an ability to encapsulate a wide range of differently charged species, including organic molecules, transition metal complexes, and "ship-in-a-bottle" nanoclusters not observed otherwise.