Crystallographic symmetries (přednáší Franka Miriam Brückler, Zagreb)

Abstrakt:
Symmetry is a mathematical concept fundamental for crystallography. Crystals are classified according to, and many of their physical and chemical properties depend on their outer and inner symmetry. Obviously, crystals are bounded three-dimensional objects, so the possible symmetries of their outer shapes are found in the symmetry classes of three-dimensional bodies. However, the inner periodicity of crystal structures limits the possible inner, and consequently outer symmetries of crystals. In particular, no crystal (neither the periodic inner structure nor the visible macroscopic crystal) can posess rotational symmetries of orders different from 1, 2, 3, 4, and 6; this is the so-called crystallographic restriction. In this talk we shall present fundamental facts about crystal symmetries, in particular, the classification of crystals into crystal systems, crystal classes and space groups shall be introduced in a way suitable for an audience with standard mathematical graduate knowledge (in geometry and group theory), but without pre-knowledge in crystallography.

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