Design and synthesis of metal-organic polyhedra (MOPs) with targeted geometries from predetermined secondary building units (SBUs) is a long-standing challenge in chemistry and material science. Theoretical prediction shows that there are 6 possible polyhedra from the 3-coordinated, 4-coordinated octahedron ((3,4)-c octahedron) to (3,5)-c icosahedron with minimal transitivity (simplest possible). Except for one missing polyhedron (mtr) due to the unfavorable angles, we report five MOPs based on these structures, including an octahedral (3,4)-c VMOP-21 (rdo), an icosahedral (3,5)-c VMOP-25 (trc), and three intermediate derived trinodal (3,4,5)-c VMOP-22-24 (ghm, hmg, xum). Remarkably, all these MOPs obey the minimal transitivity principle and are consistent with geometrical predictions.
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