Understanding how neural circuits process and interpret information can be challenging, as connectivity and activity continuously influence each other. Activity-dependent synaptic plasticity shapes and refines this intricate relationship. Connectivity motifs, small subnetworks of a few neurons, have been found to play a key role in linking circuit structure to the dynamical properties of neural activity, such as covariability and dimensionality. Significant progress has been made in measuring precise neural connectivity; multipatch experiments and recent connectomic studies have quantified three-neuron (triplet) connectivity motifs in various brain regions and animals, revealing heterogeneous nonrandom motif distributions. However, the synaptic plasticity mechanisms underlying the formation of these specific structures remain unclear. In this work, we investigated the emergence of triplet motifs using a parametrized family of spike-timing-dependent plasticity (STDP) rules, including Hebbian-like, anti-Hebbian-like, and symmetric rules, thus taking into account different types of spike-timing interactions. We developed an analytical framework to relate the STDP parameters to triplet connectivity motifs, allowing us to predict which motifs can emerge from any given STDP rule. Our results show that no single STDP rule alone can generate the entire set of triplet motifs. However, combining different STDP rules facilitates the formation of all possible triplet motifs. This suggests that neural circuits use a diversity of plasticity rules to achieve multiple connectivity motifs observed in the data. Our analytical predictions are supported by simulations in large networks. In conclusion, our work unravels the role of synaptic plasticity in shaping triplet connectivity structures, highlights the importance of heterogeneity in models of biological circuits, and provides a foundation for further investigation into the interplay between plasticity and dynamics.