Structural DNA nanotechnology(1-4) and the DNA origami technique(5), in particular, have provided a range of spatially addressable two-and three-dimensional nanostructures(6-10). These structures are, however, typically formed of tightly packed parallel helices(5-9). The development of wireframe structures(10,11) should allow the creation of novel designs with unique functionalities, but engineering complex wireframe architectures with arbitrarily designed connections between selected vertices in three-dimensional space remains a challenge. Here, we report a design strategy for fabricating finite-size wireframe DNA nanostructures with high complexity and programmability. In our approach, the vertices are represented by n x 4 multi-arm junctions (n = 2-10) with controlled angles, and the lines are represented by antiparallel DNA crossover tiles(12) of variable lengths. Scaffold strands are used to integrate the vertices and lines into fully assembled structures displaying intricate architectures. To demonstrate the versatility of the technique, a series of two-dimensional designs including quasi-crystalline patterns and curvilinear arrays or variable curvatures, and three-dimensional designs including a complex snub cube and a reconfigurable Archimedean solid were constructed.