Excellent seeing, coronal conditions, and very low IR thermal background are qualities of the Dome C/Concordia station site that will allow unique solar astrophysics science. We review the science case for inner corona observations (onset of the coronal heating mechanism still poorly understood) and the promises of high angular resolution to disentangle the possible mechanisms at work between waves, convection, and reconnection in this particularly magnetically structured solar atmosphere between the high chromosphere and inner corona. For coronagraphy, IR and high resolution possibilities, Dome C is a case by itself between classical ground-based sites and space opportunities. Telescopes from 50 cm (coronagraphy oriented) to 4 m (full high resolution advantage including IR access) are proposed to benefit from these remarkable observing capabilities. Using 3 × Ø50 cm off-axis telescopes, we first propose a medium size facility (1.4 m equivalent telescope) for very high resolution access, ADSIIC (Antarctica Demonstrator of Solar Interferometric Imaging & Coronagraphy), before the ultimate 9-telescope Solar Facility equivalent to a 4 m diameter telescope: A-FOURMI (Antarctica 4 m Interferometer). Finally, 30 m tower designs and their logistics using standard containers and elementary elements of 6 m maximum length, are presented and discussed. These towers are indeed of general interest also for the other optical and IR telescopes intended for Dome C/Concordia, allowing to get over most of the turbulent ground layer and to reach the best possible permanent seeing conditions (better than half an arcsec).