Molecules and crystals with both icosahedral and cubic symmetry

Jorge Echeverría; David Casanova; Miquel Llunell; Pere Alemany; Santiago Alvarez

doi:10.1039/B719615F

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Molecules and crystals with both icosahedral and cubic symmetry†‡

Jorge Echeverría,^a David Casanova,^a Miquel Llunell,^a Pere Alemany^a and Santiago Alvarez*^a

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* Corresponding authors

^a Departament de Química Inorgànica, Departament de Química Fisica and Institut de Química Teòrica i Computacional, Universitat de Barcelona, Martí i Franquès 1- 11, Barcelona, Spain

Abstract

Notwithstanding the apparent incompatibility between octahedral and icosahedral symmetries, fragments with the two types of symmetry coexist in many molecules and crystals, as evidenced by continuous shape and symmetry measures. A geometric analysis of Platonic and Archimedean polyhedra and of a variety of molecular and crystal structures strongly suggests that octahedral symmetry is latent in icosahedral polyhedra and vice versa. In this Feature Article, new concepts and structural data from the literature combine to offer a perspective view of complex molecular and extended structures. Its influence on the common cubic packing of icosahedral molecules is discussed for a variety of examples, including water clathrates, dodecahedrane, Buckminsterfullerene, the Pd₁₄₅ and Mo₁₃₂ clusters and several intermetallic phases.

Kepler stared, weeping, at the five polyhedrafit into each other, systematic, perfect,with musical order up to the great sphere.He loved the dodecahedron, wept over the icosahedronfor its inconsistencies and intricacieslovely and odd but, oh!, so necessary,since one cannot conceive more perfect solidsbeyond the five known, in three dimensions. Gabriel Celaya

Graphical abstract: Molecules and crystals with both icosahedral and cubic symmetry

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Supplementary files

Table S1: Shape measures of the M ₈ and X ₁₂ groups relative to the cube and the icosahedron, respectively, in the family of compounds of general formula [M ₈(AX ₂) ₆]. Fig. S2: Representation of one plane of the Cs ₈Sn ₄₆ structure showing four of the six edge-sharing Cs ₁₂ icosahedra connected to the central one that are responsible for a primitive cubic packing. Fig. S3: Perspective view of the nearly perfect cuboctahedral arrangement of the nearest neighbour (H ₂O) ₆₀ clusters that form part of the (H ₂O) ₁₀₀ nanodrops in the guanidinium salt of a Mo ₁₃₂ complex PDF (3078K)

Article information

DOI: https://doi.org/10.1039/B719615F
Article type: Feature Article
Submitted: 19 Dec 2007
Accepted: 21 Feb 2008
First published: 01 May 2008

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Chem. Commun., 2008, 2717-2725

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Molecules and crystals with both icosahedral and cubic symmetry

J. Echeverría, D. Casanova, M. Llunell, P. Alemany and S. Alvarez, Chem. Commun., 2008, 2717 DOI: 10.1039/B719615F

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Chemical Communications

Molecules and crystals with both icosahedral and cubic symmetry†‡

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Molecules and crystals with both icosahedral and cubic symmetry

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