In the present work, we discuss the role of block copolymers in the self-assembly of diblock copolymers and monodisperse colloidal polymeric particles. Experiments for this type of system were carried out on colloidal dispersions of polystyrene (PS) colloidal particles and polystyrene-poly(2-vinylpyridine) (PS-PVP) block copolymers in ethanol. After complete solvent evaporation and upon annealing at temperatures above the glass transition temperature of both PS and PVP, the system-assembles into closely packed PS polyhedrons surrounded by a PVP phase. A three-step mechanism is suggested for the rearrangement of the system, based on the segregation of block copolymers at the colloidal surface, penetration of PS blocks into the PS colloids, and frustration and relaxation of the PVP chains with subsequent relaxation of the colloid. A simple mathematical model is proposed for the packing frustration of the PS-PVP block copolymers, which allows a direct benchmark of the suggested mechanism with the experimental evidence for the colloidal system investigated.