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Knowledge of the three-dimensional structure of Galactic molecular clouds is important for understanding how clouds are affected by processes such as turbulence and magnetic fields and how this structure affects star formation within them. Great progress has been made in this field with the arrival of the Gaia mission, which provides accurate distances to ∼109 stars. Combining these distances with extinctions inferred from optical–infrared, we recover the three-dimensional structure of 16 Galactic molecular cloud complexes at ∼1 pc resolution using our novel three-dimensional dust mapping algorithm dustribution. Using astrodendro , we derive a catalogue of physical parameters for each complex. We recover structures with aspect ratios between 1 and 11, i.e. everything from near-spherical to very elongated shapes. We find a large variation in cloud environments that is not apparent when studying them in two dimensions. For example, the nearby California and Orion A clouds look similar on sky, but we find California to be more sheet-like, and massive, which could explain their different star formation rates. By calculating the total mass of these individual clouds, we demonstrate that it is necessary to define cloud boundaries in three dimensions in order to obtain an accurate mass; simply integrating the extinction overestimates masses. We find that Larson's relationship on mass versus radius holds true whether you assume a spherical shape for the cloud or take their true extents. [ABSTRACT FROM AUTHOR]