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Formation of Ge-rich prismatic inclusions in the hexagonal SiGe shell of GaP-Si-SiGe nanowires is reported and discussed in relation to a growth model that explains their origin. An accurate TEM/EDX analysis shows that such prisms develop right on top of any {112[combining macron]0} facet present on the inner GaP-Si surface, with the base matching the whole facet extension, as large as tens of nanometers, and extending within the SiGe shell up to a thickness of comparable size. An enrichment in Ge by around 5% is recognized within such regions. A phase-field growth model, tackling both the morphological and compositional evolution of the SiGe shell during growth, is exploited to assess the mechanism behind the prism formation. A kinetic segregation process, stemming from the difference in surface mobility between Ge (faster) and Si (slower), is shown to take place, in combination with the evolution of the SiGe shell morphology. Actually, the latter moves from the one templated by the underlying GaP-Si core, including both {101[combining macron]0} and {112[combining macron]0} facets, to the more energetically convenient hexagon, bounded by {101[combining macron]0} facets only. Simulations are shown to accurately reproduce the experimental observations for both regular and asymmetric nanowires. It is then discussed how a careful control of the GaP core faceting, as well as a proper modulation of the shell growth rate, allows for direct control of the appearance and size of the Ge-rich prisms. This tunability paves the way for a possible exploitation of these lower-gap regions for advanced designs of band-gap-engineering.