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The reaction of cis-blocked, square-planar M-II complexes with tetratopic N-donor ligands is known to give metallasupramolecular assemblies of the formula M2nLn. These assemblies typically adopt barrel-like structures, with the ligands paneling the sides of the barrels. However, alternative structures are possible, as demonstrated by the recent discovery of a Pt8L4 cage with unusual gyrobifastigium-like geometry. To date, the factors that govern the assembly of (M2nLn)-L-II complexes are not well understood. Herein, we provide a geometric analysis of M2nLn complexes, and we discuss how size and geometry of the ligand is expected to influence the self-assembly process. The theoretical analysis is complemented by experimental studies using different cis-blocked Pt-II complexes and metalloligands with four divergent pyridyl groups. Mononuclear metalloligands gave mainly assemblies of type Pt8L4, which adopt barrel- or gyrobifastigium-like structures. Larger assemblies can also form, as evidenced by the crystallographic characterization of a Pt10L5 complex and a Pt16L8 complex. The former adopts a pentagonal barrel structure, whereas the latter displays a barrel structure with a distorted square orthobicupola geometry. The Pt16L8 complex has a molecular weight of more than 23 kDa and a diameter of 4.5 nm, making it the largest, structurally characterized M2nLn complex described to date. A dinuclear metalloligand was employed for the targeted synthesis of pentagonal Pt10L5 barrels, which are formed in nearly quantitative yields.