A model for the structure of the zeolite SSZ-31 is presented. The model is obtained by combining information from adsorption capacity measurements, transmission electron microscopy, and high-resolution X-ray diffraction. SSZ-31 is a one-dimensional large-pore zeolite with a framework density of 18.7 tetrahedral(T)-atoms per nm-3 and a bulk density of 1.87 g cm-3. The pore apertures are elliptical with major and minor axes of approximately 8.6 Å x 5.7 Å. SSZ-31 is an extreme example of a complex and highly faulted zeolite. The structure can be described as an intergrowth of four different but structurally related polymorphs.