The Marriage of Sierpiński Triangles and Platonic Polyhedra

Abstract

Fractal structures with self-similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry-directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpiński tetrahedron ST-T and the Sierpiński octahedron ST-O, in which each possesses a fractal Sierpiński triangle on their independent faces. These two discrete complexes are formed in near-quantitative yield from the multi-component self-assembly of truncated Sierpiński triangular kernel L¹ with tribenzotriquinacene-based hexatopic and anthracene-based tetratopic terpyridine ligands (L³ and L⁴ ) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS² ). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules.