A Keplerian Ag<sub>90</sub> nest of Platonic and Archimedean polyhedra in different symmetry groups.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 32620807.
- Also identified by DOI 10.1038/s41467-020-17198-1 and PMC identifier 7335041.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
Polyhedra are ubiquitous in chemistry, biology, mathematics and other disciplines. Coordination-driven self-assembly has created molecules mimicking Platonic, Archimedean and even Goldberg polyhedra, however, nesting multiple polyhedra in one cluster is challenging, not only for synthesis but also for determining the alignment of the polyhedra. Here, we synthesize a nested Ag<sub>90</sub> nanocluster under solvothermal condition. This pseudo-T<sub>h</sub> symmetric Ag<sub>90</sub> ball contains three concentric Ag polyhedra with apparently incompatible symmetry. Specifically, the inner (Ag<sub>6</sub>) and middle (Ag<sub>24</sub>) shells are octahedral (O<sub>h</sub>), an octahedron (a Platonic solid with six 3.3.3.3 vertices) and a truncated octahedron (an Archimedean solid with twenty-four 4.6.6 vertices), whereas the outer (Ag<sub>60</sub>) shell is icosahedral (I<sub>h</sub>), a rhombicosidodecahedron (an Archimedean solid with sixty 3.4.5.4 vertices). The Ag<sub>90</sub> nanocluster solves the apparent incompatibility with the most symmetric arrangement of 2- and 3-fold rotational axes, similar to the arrangement in the model called Kepler's Kosmos, devised by the mathematician John Conway.