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.