Dodecahedron–icosahedral system

Voytekhovsky Yu. L.

Zapiski RMO (Proceedings of the Russian Mineralogical Society). 2020. V. 149. N 6. P. 101-109

https://doi.org/10.31857/S0869605520060155

Full text is available on eLIBRARY.RU

Language: Russian 

Abstract

The lattice structure of crystals forbids the 5^th order symmetry axes. Therefore, a dodecahedron and an icosahedron were excluded from the set of crystalline forms by R.J. Hauy. Later, J.B. Rome de Lisle showed by goniometric measurements that the well-known “dodecahedron” and “icosahedron” of pyrite are the pentagonal dodecahedron and its combination with the octahedron. Nevertheless, E.S. Fedorov and V.V. Dolivo-Dobrovolsky considered the dodecahedron–icosahedral system to be very close to the cubic system (with 4L₃, 3L₂, and 3Р in the same orientation). Over the past few decades, mineralogy and crystallography have conceptually and methodically mastered exotic objects (shechtmanites, fullerenes, capsids of icosahedral viruses) with 5^th order symmetry axes. It is proposed to include the dodecahedron– icosahedral syngony in the university course of crystallography with axial and planaxial species of symmetry.

Keywords: dodecahedron, icosahedron, syngony, point symmetry group, simple shape, 5th order symmetry axes, shechtmanite, graphene, fullerene