Abstract

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Symmetry: Culture and Science
Volume 32, Number 1, pages 041-057 (2021)
https://doi.org/10.26830/symmetry_2021_1_041

CRYSTALS AND SYMMETRY: AN HISTORICAL OUTLINE

Gert-Martin Greuel^*

^* Department of Mathematics, University of Kaiserslautern, Erwin-Schroedinger Str., Kaiserslautern, 67663, Germany.
E-mail: greuel@mathematik.uni-kl.de
Web: https://www.mathematik.uni-kl.de/greuel
ORCID: 0000-0002-2521-019X

Abstract: Crystals have always fascinated people. Not only their mysterious variety of colour refraction, but also their regular geometry and special symmetry surprise and delight repeatedly. This article will briefly outline the history of crystallography from the Platonic solids to quasicrystals and the mathematical-geometrical description of crystal structures. We also explain why the mathematical concepts of group theory are not only the unifying theoretical concept for the intuitive idea of symmetry, but also provide a standardized description of the shape and classification for the various crystals.

Keywords: crystal, symmetry, polyhedra, snowflake, lattice, crystallographic groups, group theory, quasicrystals
MSC 2010: 01-01, 97-01, 20H15

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