Design and synthesis of metal-organic polyhedra (MOPs) with targeted geometries from predetermined secondary building units (SBUs)i salong-standing challenge in chemistry and material science.T heoretical prediction shows that there are 6p ossible polyhedra from the 3-coordinated, 4coordinated octahedron ((3,4)-c octahedron) to (3,5)-c icosahedron with minimal transitivity (simplest possible). Except for one missing polyhedron (mtr)d ue to the unfavorable angles, we report five MOPs based on these structures,i ncluding an octahedral (3,4)-c VMOP-21 (rdo), an icosahedral (3,5)-c VMOP-25 (trc), and three intermediate derived trinodal (3,4, hmg, xum). Remarkably,a ll these MOPs obey the minimal transitivity principle and are consistent with geometrical predictions.