Molecules and crystals with both icosahedral and cubic symmetry.
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.
Echeverría
Jorge
J
Departament de Química Inorgànica, Departament de Química Fisica and Institut de Química Teòrica i Computacional, Universitat de Barcelona, Martí i Franquès 1- 11, 08028 Barcelona, Spain.
Casanova
David
D
Llunell
Miquel
M
Alemany
Pere
P
Alvarez
Santiago
S