Motivation: The molecular rules determine the strength and orientation (parallel or antiparallel) of interacting coiled-coil helices in protein-protein interactions. Interpreting these rules is crucial for identifying novel protein-protein interactions, designing competitive binders, and constructing large assemblies containing coiled-coil domains. This study establishes the molecular principles that dictate the strength and orientation of coiled-coil interactions, providing insights relevant to these applications. Results: We examined how hydrophobic contacts determine structural specificity within coiled-coil dimers. Our analysis revealed that the hydrophobic core densities differ between parallel and antiparallel dimer confirmations, highlighting their importance in stabilizing different structural arrangements. We developed COiled-COil aNalysis UTility (COCONUT), a computational platform with machine learning models, validated for predictive capabilities in various applications. Using COCONUT's pipeline for coiled-coil analysis and modeling, we predicted the orientation of substitution-sensitive coiled-coil dimer, identified residue pairings in non-canonical coiled-coil heterodimer, and constructed n-stranded coiled-coil model. These results demonstrate COCONUT's utility as a computational framework for interpreting and modeling coiled-coil structures. Availability and implementation: COCONUT is an open-source and free Python package available here https://github.com/neeleshsoni21/COCONUT. The documentation is available in the source code and here: https://neeleshsoni21.github.io/COCONUT/