From ligand-receptor binding to DNA hybridization, molecular recognition plays a central role in biology. Over the past several decades, chemists have successfully reproduced the exquisite specificity of biomolecular interactions. However, engineering multiple specific interactions in synthetic systems remains difficult. DNA retains its position as the best medium with which to create orthogonal, isoenergetic interactions, based on the complementarity of Watson-Crick binding. Here we show that DNA can be used to create diverse bonds using an entirely different principle: the geometric arrangement of blunt-end stacking interactions. We show that both binary codes and shape complementarity can serve as a basis for such stacking bonds, and explore their specificity, thermodynamics and binding rules. Orthogonal stacking bonds were used to connect five distinct DNA origami. This work, which demonstrates how a single attractive interaction can be developed to create diverse bonds, may guide strategies for molecular recognition in systems beyond DNA nanostructures.