We develop a model for nucleation of islands in vapor-liquid-solid nanowires with either vertical or truncated corner facets. Under the assumption of two-dimensional geometry of the growing island, it is shown that the earlier energetic condition for the truncated edge at the growth interface is modified by chemical potential. Therefore, the islands may nucleate at the trijunction during growth even if the truncation is preferred at the no growth conditions on surface energetic grounds. This conclusion may be used as the first step for understanding the peculiar oscillatory behavior of the growth interface and the related crystal phases of III-V nanowires.