Unit 4.5 - Space Groups and Space Group Symbols

Unit 4.5 of our course The Fascination of Crystals and Symmetry
Additonal resources at: crystalsymmetr...
If we consider translational symmetry only, the repeating lattices, we saw, that there are 14 different possibilities, the 14 Bravais lattices.
If we restrict symmetry considerations to macroscopic crystalline objects, discounting their potentially additional internal translational symmetry, then we end up with 32 crystal classes, describing their different kinds of outer shapes.
And if we now combine all these symmetry elements with pure translations of the lattice and the two symmetry elements with translational components, namely screw axes and glide planes, then one can show that 230 different symmetrical arrangements in 3D are possible - these are the fameous 230 space groups.
In this unit the nomenclature of space groups is introduced. Additionally, the crystallographic viewing directions are elucidated again, and finally we would like to shine some light on the relationship between the three categories ‘space group’ - ‘point group’ and finally ‘crystal system".
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