Competing noncovalent interactions play a pivotal role in the folding and assembly of three-dimensional structures, especially in flexible molecules. Calculations using density functional theory reveal that two squaramide rings aggregate to form a slipped antiparallel π-stacked dimer with high propensity. This π-π stacking interaction is used to design foldamers in which the squaramides are tethered by a simple methylene bridge, and consequently, the structure folds on to itself incorporating a "turn" element. The variation in relative energy with respect to change in dihedral angle for these foldamers show that for all the structures two rings are displaced in space and the folding potential is asymmetric, starting from seemingly symmetric molecules. The addition of successive squaramide rings connected with simple methylene bridges leads to the formation of higher-order structures with a "Turn-Stack-Turn" structural motif. The "Turn-Stack-Turn" motif can be used in designing new synthetic foldamers which could potentially mimic closely related biological systems. Further, it was found that the aggregation of the folded structures was energetically favored over the unfolded structures. The present set of calculations are important in light of the fact that these simple methylene bridged squaramide rings present synthetic challenges.