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The method extends thrust-line analysis to three-dimensional problems by finding equilibrium force networks within the vault's geometry, representing possible paths of the compression forces. Through case studies, this research demonstrates the potential of the method as a powerful tool for understanding, visualizing and exploring the equilibrium of compression-only structures. This method also has the potential to suggest three-dimensional collapse mechanisms. Its results compare to those obtained with Discrete Element Modeling (DEM) and structural 3D-printed scale models.