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I use the following code snippet to create the diamond space group in GAP with the help of cryst package:

gap> M1:=[[0, 0, 1, 0],[1, 0, 0, 0],[0, -1, 0, 0],[1/4, 1/4, 1/4, 1]];;
gap> M2:=[[0,0,-1,0],[0,-1,0,0],[1,0,0,0],[0,0,0,1]];;
gap> S:=AffineCrystGroup([M1,M2]);
<matrix group with 2 generators>

The above code snippet comes from page 21 of the book Computer Algebra and Materials Physics, as shown below:

# As for the diamond case, in the GAP computation, the 
# crystallographic group is defined as follows. (The minimal
# generating set is used for simplicity.)
gap> M1:=[[0,0,1,0],[1,0,0,0],[0,-1,0,0],[1/4,1/4,1/4,1]];;
gap> M2:=[[0,0,-1,0],[0,-1,0,0],[1,0,0,0],[0,0,0,1]];;
gap> S:=AffineCrystGroup([M1,M2]);
<matrix group with 2 generators>
gap> P:=PointGroup(S);
Group([ [ [ 0, 0, 1 ], [ 1, 0, 0 ], [ 0, -1, 0 ] ],
[ [ 0, 0, -1 ], [ 0, -1, 0 ], [ 1, 0, 0 ] ] ])

It's well-known that diamond has the space group Fd-3m (No. 227). I wonder how I can verify/confirm/check this fact in GAP after I've created the above AffineCrystGroup.

Regards, HZ

Hongyi Zhao
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  • This question might be better suited for https://math.stackexchange.com/questions/tagged/crystallography – Olexandr Konovalov May 20 '22 at 19:42
  • Ah, I see! I didn't know that rule. See https://math.meta.stackexchange.com/questions/20982/problem-you-have-reached-your-question-limit and https://math.stackexchange.com/help/question-bans for some tips. In particular, you could try to edit one of your downvoted or closed questions. Closed questions will be placed in the review queue for reopening after you edit them. – Olexandr Konovalov May 21 '22 at 09:37
  • Also, where `M1` and `M2` are coming from? – Olexandr Konovalov May 21 '22 at 09:42
  • 1. Thank you for the tips. 2. I have added descriptions of their source material. – Hongyi Zhao May 21 '22 at 10:24
  • 1) Screenshots instead of text are usually frowned upon. They are not searchable and not editable. 2) https://math.stackexchange.com/ has LaTeX support while this site is not. 3) This is really a question that belongs to https://math.stackexchange.com/ and not here. You have two sources with different generating sets for apparently the same group, and you would like to check that they are equivalent. I suggest to try to improve your profile to be able to post it at https://math.stackexchange.com/. – Olexandr Konovalov May 21 '22 at 10:41
  • By saying `improve your profile`, do you mean `edit one of your downvoted or closed questions`, as you suggested above? – Hongyi Zhao May 21 '22 at 10:48
  • Yes - you need to overcome the question limit, and that seems to be the way to do this. – Olexandr Konovalov May 21 '22 at 12:57
  • @OlexandrKonovalov I've reposted the question [here](https://math.stackexchange.com/questions/4450721/identify-the-space-group-international-table-number-from-the-group-created-by-af). – Hongyi Zhao May 24 '22 at 02:43
  • No, please don't vandalise old questions this way. That was a proper question, useful, although closed. I've reverted your attempt. You need to ask a new one. "Edit" in "edit one of your downvoted or closed questions" means "edit to improve it", not "edit to replace by a completely different question". – Olexandr Konovalov May 24 '22 at 10:24
  • It seems that it is not easy for me to do what you describe at present. All the questions I have asked are actually not easy to polish from this perspective, at least in my current opinion. – Hongyi Zhao May 24 '22 at 23:24

1 Answers1

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Based on the command ConjugatorSpaceGroups provided by the cryst package, as described here, I figured out the following solution:

gap> M1OnRight:=[[0,0,1,0],[1,0,0,0],[0,-1,0,0],[1/4,1/4,1/4,1]];;
gap> M2OnRight:=[[0,0,-1,0],[0,-1,0,0],[1,0,0,0],[0,0,0,1]];;
gap> SG227OnRight:=AffineCrystGroupOnRight([M1OnRight,M2OnRight]);
<matrix group with 2 generators>
gap> ConjugatorSpaceGroups(SG227OnRight, SpaceGroupOnRightIT(3,227));
[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 3/8, 3/8, 7/8, 1 ] ]
Hongyi Zhao
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