We report the design and synthesis of two metal-organic frameworks (MOFs) with permanent porosity, MOF-818 and MOF-919, using a small ditopic organic linker, 1H-pyrazole-4-carboxylic acid (H2PyC), 0.4 nm in length. Three mesoporous cages of unprecedented polyhedra are identified in these MOFs, a wuh cage in MOF-818 and yys and liu cages in MOF-919, with diameters of 3.8, 4.9, and 6.0 nm, respectively. The ditopic H2PyC linker functions as the edge in the structure, while two types of metal-containing second building units (SBUs) function as the vertices. 28 vertices are present in the wuh cage; 50 in the yys cage; and 70 in the liu cage. Systematic analysis of these cages along with other mesoporous cages in supramolecules and MOFs constructed by ditopic linkers reveals that the extension of cage size is dictated by both the number and connectivity of the vertices. The increase in cage size is proportional to the number of vertices, while the growth rate is determined by their connectivity. The reduction in connectivity is found to be an effective way to create large cages. All three cages in this report are constructed by three-connecting (3-c) vertices and two-connecting (2-c) vertices. This [2-c, 3-c] connectivity represents the least connectivity required for the construction of cages and the most effective one for cage size expansion. The largest cage, liu, exhibits a cage size to linker size ratio of 15, outstanding in supramolecules and MOFs. MOF-818 is stable in water with a wide pH range (pH = 2-12), and the wuh cage is big enough for the inclusion of biomolecules such as vitamin B-12 and insulin.