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We investigate the fundamental optical properties of single zinc-blende InP/ZnSe/ZnS nanocrystals (NCs) using frequency- and time-resolved magneto-photoluminescence spectroscopy. At liquid helium temperature, highly resolved spectral fingerprints are obtained and identified as the recombination lines of the three lowest states of the band-edge exciton fine structure. The evolutions of the photoluminescence spectra and decays under magnetic fields show evidence for a ground dark exciton level 0L with zero angular momentum projection along the NC main elongation axis. It lies 300 to 600 μeV below the ±1L bright exciton doublet, which is finely split by the NC shape anisotropy. These spectroscopic findings are well reproduced with a model of exciton fine structure accounting for shape anisotropy of the InP core. Our spectral fingerprints are extremely sensitive to the NC morphologies and unveil highly uniform shapes with prolate deviations of less than 3% from perfect sphericity.