The structure and growth of crystal nuclei that spontaneously form during computer simulations of the simplest nontrivial model of a liquid, the hard sphere system, is described in this work. Compact crystal nuclei are observed to form at densities within the coexistence region of the phase diagram. The nuclei possess a range of morphologies with a predominance of multiply twinned particles possessing in some cases a significant decahedral character. However the multiply twinned particles do not form from an initial decahedral core but appear to nucleate as blocks of a face-centered cubic crystal partially bounded by stacking faults.