Polyhedral colloidal clusters assembled from functional inorganic nanoparticles have attracted great interest in both scientific research and applications. However, the spontaneous assembly of colloidal nanoparticles into polyhedral clusters with regular shape and tunable structures remains a grand challenges. Here, we successfully construct Mackay icosahedral and regular tetrahedral colloidal clusters assembled from gold nanoparticles grafted with a mixture of polystyrene (PS) and poly(2-vinylpyridine) (P2VP) homopolymers by precisely tuning the interfacial interaction between the nanoparticles and the oil/water interface. By increasing the proportion of hydrophilic P2VP ligands on the surface of gold nanoparticles, the Mackay icosahedral clusters can transform into regular tetrahedral clusters in order to maximize the surface area of the polyhedral assembly. Furthermore, we reveal the formation mechanism of these regular polyhedral colloidal clusters. The formation of polyhedral colloidal clusters is not only dependent on the entropy but also determined by the interfacial free energy. This finding demonstrates an effective approach to organize nanoparticles into polyhedral colloidal clusters with potential applications in various fields.