We present a detailed study of the dwarf galaxy VV124 (UGC4879), recently recognized as a remarkably isolated member of the Local Group. We have obtained deep (r ≃ 26.5) wide-field (23' × 23') g,r photometry of individual stars with the LBC camera at the Large Binocular Telescope under sub-arcsec seeing conditions. The color-magnitude diagram suggests that the stellar content of the galaxy is dominated by an old, metal-poor population, with a significant metallicity spread. A very clean detection of the RGB tip allows us to derive an accurate distance of D = 1.3 ± 0.1 Mpc. Combining surface photometry with star counts, we are able to trace the surface brightness profile of VV124 out to ~5' ≃ 1.9 kpc radius (where μr ≃ 30 mag/arcsec2), showing that it is much more extended than previously believed. Moreover, the surface density map reveals the presence of two symmetric flattened wings emanating from the central elongated spheroid and aligned with its major axis, resembling a stellar disk seen nearly edge-on. We also present H i observations obtained with the Westerbork Synthesis Radio Telescope (WSRT), the first ever of this object. A total amount of ≃ 106 M&sun; of H i gas is detected in VV124. Compared to the total luminosity, this gives a value of MHI/LV = 0.11, which is particularly low for isolated Local Group dwarfs. The spatial distribution of the gas does not correlate with the observed stellar wings. The systemic velocity of the H i in the region superposed to the stellar main body of the galaxy is Vh = -25 km s-1. The velocity field shows substructures typical of galaxies of this size but no sign of rotation. The H i spectra indicates the presence of a two-phase interstellar medium, again typical of many dwarf galaxies.