By using the supermolecular building block (SBB) strategy, a polyhedron-based metal-organic framework (PMOF), which features three types of cages with multiple sizes and shapes, has been synthesized. It exhibits high performance for CO2 capture (170 cm(3) g(-1) at 273 K under 1 bar) and selectivity of CO2/CH4 (9.4) and C3H8/CH4 (271.5).