Polyhedra have attracted scientists' attentions due to their high-symmetric architectures since ancient times, and even served as common modes in natural world. Chemists in the past few centuries have strived to synthesise these polyhedral targets. Despite achievements that have been arrived, there is still a gap between the great varieties of polyhedral shapes observed in nature and the relatively limited molecular polyhedra constructed by small organic molecules. Fortunately, DNA was shown to be an excellent material in molecular construction. The construction of polyhedral structures with DNA improves the development of synthetic chemistry. This book reviews the recent progress made in the theoretical investigation of a new mathematical theory of DNA polyhedra.