Approximating the three-dimensional structure of a fault network at depth in the subsurface is key for robust estimates of fluid flow. However, only observations of two-dimensional outcrops are often available. To shed light on the relationship between two- and three-dimensional measurements of fracture networks, we examine data from a unique set of eleven X-ray synchrotron triaxial compression experiments that reveal the evolving three-dimensional fracture network throughout loading. Using machine learning, we derive relationships between the two- and three-dimensional measurements of three properties that control fluid flow: the porosity, and volume and tortuosity of the largest fracture at a particular differential stress step. The models predict the porosity and volume of the largest fracture with R² scores of >0.99, but predict the tortuosity with maximum R² scores of 0.68. To test the assumption that different rock types may require different equations between the two- and three-dimensional properties, we develop models for both individual rock types (granite, monzonite, marble, sandstone) and all of the experiments. Models developed using all of the experiments perform better than models developed for individual rock types, suggesting fundamental similarities between fracture networks in rocks often analyzed separately. Models developed with several parallel two-dimensional observations perform similarly to models developed with several perpendicular two-dimensional observations. When the models are developed with statistics of the two-dimensional observations, the models primarily depend on the mean and median when they predict the porosity, and minimum when they predict the volume and tortuosity.