The high-temperature cubic form of bismuth oxide, δ-Bi2O3, is the best intermediate-temperature oxide-ionic conductor known. The most elegant way of stabilizing δ-Bi2O3 to room temperature, while preserving a large part of its conductivity, is by doping with higher valent transition metals to create wide solid-solutions fields with exceedingly rare and complex (3 + 3)-dimensional incommensurately modulated "hypercubic" structures. These materials remain poorly understood because no such structure has ever been quantitatively solved and refined, due to both the complexity of the problem and a lack of adequate experimental data. We have addressed this by growing a large (centimeter scale) crystal using a novel refluxing floating-zone method, collecting high-quality single-crystal neutron diffraction data, and treating its structure together with X-ray diffraction data within the superspace symmetry formalism. The structure can be understood as an "inflated" pyrochlore, in which corner-connected NbO6 octahedral chains move smoothly apart to accommodate the solid solution. While some oxide vacancies are ordered into these chains, the rest are distributed throughout a continuous three-dimensional network of wide δ-Bi2O3-like channels, explaining the high oxide-ionic conductivity compared to commensurately modulated phases in the same pseudobinary system.