Dodecahedron–icosahedral system

Voytekhovsky Yu. L.

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

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Language: Russian 


The lattice structure of crystals forbids the 5th 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 5th 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