PerspectiveQuasicrystals

Tessellating tiny tetrahedrons

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Science  21 Dec 2018:
Vol. 362, Issue 6421, pp. 1354-1355
DOI: 10.1126/science.aav8597

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Summary

Tessellating tiles and bricks of well-defined geometric shapes can be traced back to the ancient age (∼4000 BCE), when Sumerians used clay tiles to decorate building walls. Since 1619 when Johannes Kepler first wrote about tessellation, it has become a topic of interest in disciplines including pure mathematics, materials science, chemistry, art, architecture, and industrial design. Packing convex polygonal shapes into three-dimensional (3D) Euclidean space was conjectured by Ulam to form a more dense tessellation than spheres, but that conjecture was theoretically verified only recently for packing tetrahedrons in a quasicrystalline (QC) arrangement through shape-induced entropic interactions (1). Forming a QC superlattice of tetrahedrons with rotational symmetricity yet no transitional periodicity (2) has represented a grand experimental challenge. On page 1396 of this issue, Nagaoka et al. (3) report a “flexible polygon tiling rule” that guided the self-assembly of nanometer-sized tetrahedrons of cadmium chalcogenide (CdSe-CdS core-shell nanoparticles) to form a 10-fold QC superlattice at a liquid-air interface (see the figure).

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