The Marriage of Sierpinski Triangles and Platonic Polyhedra

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 Sierpinski tetrahedron ST-T and the Sierpinski octahedron ST-O, in which each possesses a fractal Sierpinski triangle on their independent faces. These two discrete complexes are formed in near-quantitative yield from the multi-component self-assembly of truncated Sierpinski triangular kernel L-1 with tribenzotriquinacene-based hexatopic and anthracene-based tetratopic terpyridine ligands (L-3 and L-4) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS(2)). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules.

Automated summary

Fractal structures with self-similarity are constructed using rational geometry-directed precursor design, resulting in two fascinating Platonic solids with Sierpinski triangles. These discrete complexes are formed through multi-component self-assembly and exhibit enhanced stabilities. This study provides new constructs for simulating complex virus assemblies and molecular encapsulation.