We have developed a utility to both stitch cube maps into other types of texture maps (equirectangular, dual paraboloid, and octahedral), and stitch those other types back into cube maps. The utility allows for flexibility in the image size of the conversion - the user can specify the desired image width, and the height is computed (cube, paraboloid, and octahedral mappings are square, and spherical maps are generated to have 16:9 aspect ratio). Moreover, the utility is sampling-agnostic, so the user can select whether to use uniform or jittered sampling over the pixels, as well as the number of samples to use per pixel. The rest of this paper discusses the mathematical framework for projecting from cube maps to equirectangular, dual paraboloid, and octahedral environment maps, as well as the mathematical framework for the inverse projections. We also describe two sampling techniques: uniform sampling and correlated multi-jittered sampling. We perform an evaluation of the sampling techniques and a comparative analysis of the different projections using objective image quality assessment metrics.