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gap-packages / cryst

Computing with crystallographic groups
https://www.math.uni-bielefeld.de/~gaehler/gap/packages.php#Cryst
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Affine crystallographic groups vs space groups. #36

Closed hongyi-zhao closed 1 year ago

hongyi-zhao commented 1 year ago

I noticed the following description here:

Cryst provides a rich set of methods to compute with affine crystallographic groups, in particular space groups.

For a long time, I have been puzzled by the subtle differences and connections between the two terms: Affine crystallographic groups and space groups. So, what are the differences and connections between them?

Regards, Zhao

gaehler commented 1 year ago

Space groups have a translation subgroup of full rank d, whereas general affine crystallographic groups may have a translation subgroup of smaller rank.