Metal–organic polyhedra (MOPs) have attracted great interest in the past decade. As a new series of nano-material, MOPs have high outer and inner specific surface areas and are able to be applied in different areas such as catalysis, gas sequestration, drug delivery, molecule sensing, etc. In this review, the focus is made on the design and synthetic strategies approaching edge-bridged tetrahedra MnL6 and face-capped tetrahedra MnL4. Besides the synthesis, structure, and properties of tetrahedral self-assemblies are also considered, while tetrahedra will be compared with other complicated multinuclear constructions. The discussion of how the properties of tetrahedral cages can be altered by varying employed subcomponents is made. Moreover, the multifarious host–guest system and behavior of metal–organic tetrahedral self-assemblies for catalytic applications are addressed in details.
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