The revolution in cryo-electron microscopy has resulted in unprecedented power to resolve large macromolecular complexes including viruses. Many methods exist to explain density corresponding to proteins and thus entire protein capsids have been solved at the all-atom level. However methods for nucleic acids lag behind, and no all-atom viral double-stranded DNA genomes have been published at all. We here present a method which exploits the spiral winding patterns of DNA in icosahedral capsids. The method quickly generates shells of DNA wound in user-specified, idealized spherical or cylindrical spirals. For transition regions, the method allows guided semiflexible fitting. For the kuravirus SU10, our method explains most of the density in a semiautomated fashion. The results suggest rules for DNA turns in the end caps under which two discrete parameters determine the capsid inner diameter. We suggest that other kuraviruses viruses may follow the same winding scheme, producing a discrete rather than continuous spectrum of capsid inner diameters. Our software may be used to explain the published density maps of other double-stranded DNA viruses and uncover their genome packaging principles. Graphical Abstract