For the first time, we have used phase-contrast X-ray tomography to characterize the three-dimensional (3d) structure of cardiac tissue from patients who succumbed to Covid-19. By extending conventional histopathological examination by a third dimension, the delicate pathological changes of the vascular system of severe Covid-19 progressions can be analyzed, fully quantified and compared to other types of viral myocarditis and controls. To this end, cardiac samples with a cross-section of 3.5mm were scanned at a laboratory setup as well as at a parallel beam setup at a synchrotron radiation facility the synchrotron in a parallel beam configuration. The vascular network was segmented by a deep learning architecture suitable for 3d datasets (V-net), trained by sparse manual annotations. Pathological alterations of vessels, concerning the variation of diameters and the amount of small holes, were observed, indicative of elevated occurrence of intussusceptive angiogenesis, also confirmed by high-resolution cone beam X-ray tomography and scanning electron microscopy. Furthermore, we implemented a fully automated analysis of the tissue structure in the form of shape measures based on the structure tensor. The corresponding distributions show that the histopathology of Covid-19 differs from both influenza and typical coxsackie virus myocarditis.