The purpose of this study is to characterize experimentally the whole shape of the growth cells displayed in directional solidification and its evolution with respect to control parameters. A library of cells is first built up from observation of directional solidification of a succinonitrile alloy in a large range of pulling velocity, cell spacing, and thermal gradient. Cell boundaries are then extracted from these images and fitted by trial functions on their whole profile, from cell tip to cell grooves. A coherent evolution of the fit parameters with the control parameters is evidenced. It enables us to characterize the whole cell shape by a single function involving only two parameters which vary smoothly in the control parameter space. This, in particular, evidences a continuous evolution of the cell geometry at the cell to dendrite transition which denies the existence of a change of branch of solutions at the occurrence of sidebranching. More generally, this global determination of cell shape complemented with a previous determination of the position of cells in the thermal field (the cell tip undercooling) provides a complete characterization of growth solutions and of their evolutions in this system. It thus brings about a relevant framework for testing and improving theoretical and numerical understanding of cell shapes and cell stability in directional solidification.