The assembly, structure, and stability of DNA nanocages with the shape of truncated octahedra have been studied. The cages are composed of 12 double-stranded B-DNA helices interrupted by single-stranded linkers of thymidines of varying length that constitute the truncated corners of the structure. The structures assemble with a high efficiency in a one-step procedure, compared to previously published structures of similar complexity. The structures of the cages were determined by small-angle X-ray scattering. With increasing linker length, there is a systematic increase of the cage size and decrease of the twist angle of the double helices with respect to the symmetry planes of the cage structure. In the present study, we demonstrate the length of the single-stranded linker regions, which impose a certain degree of flexibility to the structure, to be the important determinant for efficient assembly. The linker length can be decreased to three thymidines without affecting assembly yield or the overall structural characteristics of the DNA cages. A linker length of two thymidines represents a sharp cutoff abolishing cage assembly. This is supported by energy minimization calculations suggesting substantial hydrogen bond deformation in a cage with linkers of two thymidines.