The pteropod Cuvierina constructs very lightweight, thin, flexible, and resistant shells with the most unusual microstructure: densely packed, continuous crystalline aragonite fibers that coil helically around axes perpendicular to the shell surface. The high degree of fiber intergrowth results in a particular interlocking structure. The shell is constructed by guided self-assembly, outside the animal's soft body. A prerequisite to understand its formation is to resolve the underlying crystallographic building principle. This is basic in order to use this hierarchically structured and highly functional biomaterial as inspiration for the production of new materials. It teaches us about the optimization of structures over millions of years of evolution under strict consideration of energetic costs and efficient use of available resources and materials. We have described how helical coiling proceeds by using a combination of diffraction and imaging techniques, which complement at different levels of resolution. Despite their curling, the fibers are continuously crystalline and show a preferred crystallographic growth direction. When the latter can no more be maintained due to the imposed curving, abrupt changes across twins permit to continue growth in the desired direction. This is a nice example of how crystallographically continuous fibers can grow helically.