A porous polyhedral metal-organic framework has been constructed by utilizing Zn2(COO)4 and Zn2(COO)3 SBUs as nodes and the flexible hexacarboxylate as linkers. The framework contains four types of interconnected polyhedral cages, rhombic dodecahedron, tetrahedron, octahedron, and distorted tetragonal prism. To identify the topology of the whole network, the four types of polyhedral cages can be viewed as nodes, and the whole network is signed as a (6,6,12,12) network. In another view of point, the Zn2(COO)3 SBU, Zn2(COO)4 SBU and hexacarboxylate ligands can also be considered as nodes, then the network is simply signed as a (3,4,6)-connected net with a Schlafli symbol (43) (4462) (4679).