An entirely double stranded truncated octahedral DNA nanocage structure has been modeled in silico and the molecular dynamics simulation technique has been used to characterize its dynamical properties. In this polyhedron, unlike other previously simulated truncated octahedral cages, the linker regions are represented by double helices. Simulations of nanocages, with single or double stranded linkers, have been carried out to evaluate differences in their dynamic behavior. The results indicate a higher rigidity of the double stranded nanocage in comparison with the structure sharing the same geometry but having single stranded linkers. In detail the highly constrained geometry of the entirely double stranded DNA cage generates a distortion of the polyhedron and a fixed orientation of the double helices that results in constant exposure of selected bases on the cage external surface. These bases may represent the preferential sites for chemical modifications endowing the structure with specific molecular recognition capabilities.