By the means of point-group symmetry classification, the presence of mirror planes, and/or inversion centres make the five Platonic solids achiral, whereas the Archimedean solids can be classified into thirteen types, mostly with Td, Oh, or Ih symmetry groups, except the snub cube (O) and snub dodecahedron (I), where the absence of inversion or mirror symmetries and the presence of only axial symmetries afford the chiral attributes. Generally, the MOCs expand around the design and application of the Platonic geometries (Figure ), with single ligands defining the edges and the faces of the polyhedron (homoleptic cages). However, biomolecules and high-value synthetic compounds are rarely highly symmetrical species, which urges the construction of MOCs with interior cavities of reduced symmetry, incorporating multiple ligands into the structurally intriguing Archimedean solids. However, a particular challenge in this approach is to ensure that different building blocks integrate into a single product (integrative self-sorting) rather than segregating into simpler structures (narcissistic sorting) or a statistical distribution of products (social sorting ). However, for this review, we mainly focus on the homoleptic tetrahedral, cubic, and octahedral assemblies.