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At high concentration, long Watson/Crick (WC) double-helixed DNA forms columnar crystal or liquid crystal phases of linear, parallel duplex chains packed on periodic lattices. This can also be a structural motif of short NA oligomers such as the 5’-GTAC-3’ studied here, which makes four-base WC duplexes having hydrophobic blunt ends. End-to-end aggregation then assembles these duplexes into columns and columnar phases are stabilized, in spite of breaks in the double helix every four bases. But the new degrees of freedom introduced by such breaks also enable opportunities for a more diverse palette of self-assembly modes, producing striking self-assemblies of DNA that would not be achievable with contiguous polymers. These include recently reported three-dimensional (3D) periodic low-density nanoscale networks of GCCG, and the twist grain boundary (TGB) phase presented here. In the TGB, columns of GTAC pairs assemble into monolayer sheets in which the duplex columns are mutually parallel. However, unlike in the columnar crystals, these sheets stack in helical fashion into lamellar arrays in which the column axis of each layer is rotated through a 60° angle with respect to the columns in neighboring layers. This assembly of DNA is unique in that it the fills a 3D volume wherein the major grooves of columns in each layer mutually enter and interlock with the major grooves of columns in neighboring layers. This locking is optimized by small adjustments in structure enabled by the breaks in the duplex backbones.