This is an announcement for the paper "Geometry of Banach spaces with an octahedral norm" by Rainis Haller and Johann Langemets. Abstract: We discuss the geometry of Banach spaces whose norm is octahedral or, more generally, locally or weakly octahedral. Our main results characterize these spaces in terms of covering of the unit ball. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B22 Submitted from: johann.langemets@ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.3612 or http://arXiv.org/abs/1401.3612