Talk:Frieze group

message: This numbering by 1, 2, ... 7, is this standard notation? If not, doesn't it add an extra layer of confusion where unnecessary? Dmharvey Talk 10:00, 10 August 2005 (UTC)
thread_title:  numbering of groups 

message: I'm trying to collect some photos to work into this article...
=== group 1 ===
=== group 2 ===
=== group 3 ===
=== group 4 ===
=== group 5 ===
=== group 6 ===
=== group 7 ===
Dmharvey 03:07, 12 March 2006 (UTC)
thread_title:  couple of photos 

message: Dmharvey 03:07, 12 March 2006 (UTC)
thread_title:  group 7 

message: The article says that the 7th frieze group "is isomorphic to a semidirect product of Z × C2 with C2". Isn't it also isomorphic to C2 × (the semidirect product of Z by C2)?  And isn't this a rather more helpful way of describing its structure? Maproom (talk) 13:44, 6 July 2008 (UTC)
replies: text: Every semidirect product of Z × C2 and C2 has a copy of C2 as a direct factor, and a copy of Z semi C2 as a direct complement, so I think you are right.  In fact, (the semidirect product of Z by C2) is called the infinite dihedral group so the name would definitely be nicer. JackSchmidt (talk) 16:25, 6 July 2008 (UTC)
thread_title: Abstract structure of 7th frieze group

message: Is there some reason to avoid mentioning the infinite dihedral group?  It is just group #4, like, literally, this is how dihedral groups are defined.  This also simplifies the exposition of group #7. JackSchmidt (talk) 14:00, 10 July 2008 (UTC)
replies: text: It is algebraically isomorphic (I added that), but, the way infinite dihedral groups are defined here, not as group of isometries.--Patrick (talk) 21:24, 10 July 2008 (UTC)
thread_title:  Infinite dihedral group 

message: I've come across generalizations of the frieze groups to three dimensions.
Line groups
A three-dimensional line group is a combination of an axial point group and repeats along the axis, a one-dimensional lattice. From the 7 infinite families of axial point groups, one finds 13 infinite families of line groups.
Line Groups Structure, the second chapter of Amazon.com: Line Groups in Physics: Theory and Applications to Nanotubes and Polymers (Lecture Notes in Physics) (9783642111716): Milan Damnjanovic, Ivanka Milosevic: Books
Rod groups
The 75 rod groups are the line groups whose point groups are crystallographic ones. Source: Bilbao Crystallographic Server: Subperiodic Groups: Layer, Rod and Frieze Groups Retrieval Tools
Layer groups
The 80 layer groups are subgroups of space groups; they are combinations of the crystallographic point groups with a two-dimensional lattice. Also at Bilbao.
Should I create separate articles for them or additional sections of the frieze-group article? I'd list all the rod and layer groups in them and try to describe the families of line groups.
Lpetrich (talk) 15:15, 23 June 2011 (UTC)
replies: text: I suggest, separate articles, with links from frieze group, wallpaper group, and point group. Maproom (talk) 15:28, 23 June 2011 (UTC)

text: Cool stuff! Definitely separate article(s) is/are needed. Would this Coxeter_helix "polyhedron" (helix chain of tetrahedra) have a line symmetry group? Tom Ruen (talk) 19:54, 23 June 2011 (UTC)
replies: text:  
Yes indeed, the group that I've called Cn,m -- the cyclic point group with the offsets making a helix with m turns over the the entire cycle. I've had to resort to the expedient of inventing a Schönflies-inspired notation, because my sources do not use a clear, Schönflies-style notation.  — Preceding unsigned comment added by Lpetrich (talk • contribs) 00:01, 24 June 2011 (UTC)
thread_title:  Extension to three dimensions: line, rod, and layer groups 

message: I'm having trouble correlating the IUC notation in the 3 different tables where it's used. The first large table (with purple example images) uses the term p1m1, whereas the second table (really a list called "Summarized") uses p2m1. The third table (oblique/rectangular lattice) goes back to using p1m1. Note the differences.
Here is the other instance. The 1st table uses the notation p2, the 2nd table uses p2, and the 3rd table uses p211.
I am not at all familiar with IUC notation. Is p2m1 synonymous with p1m1? Likewise, is p2 synonymous with p211? If not, then there's a typo. If so, I still think the tables should be consistent with each other. --Officiallyover (talk) 22:37, 20 February 2014 (UTC)
replies: text: On a quick look, its clear they are indexed 1-7 inconsistently, and yes p211=p2. Tom Ruen (talk) 06:54, 21 February 2014 (UTC)
thread_title:  Notation & terminology 

message: The text refers to the groups by number.  I have made this consistent with the ordering in the table, but it would be nice if the table itself were numbered for easy reference.  I'm not sure how to edit the table.  Is the markup for the table located on some other page? Will Orrick (talk) 21:29, 10 December 2015 (UTC)
replies: text: I've now realized that the table is a template that has been transcluded in the article.  It appears that, at some point, the order of the groups in the table changed, but the article did not keep pace.  Since the table is a template, it might be problematic to add numbering or make other changes that would affect other articles that transclude the template. Will Orrick (talk) 04:00, 11 December 2015 (UTC)

text: Thanks for your effort. The table is here Template:Frieze group notations, and without any indexing, but it could be added. It is also used here Orbifold_notation#Frieze_groups. It seems better to avoid indexing in the text, but if we want to include it, I guess we should look at references and see if they index, and if they are consistent. For now I moved the short indexed list before the larger table to help. Tom Ruen (talk) 06:32, 11 December 2015 (UTC)

text: I agree that it would be better to avoid indexing, if a suitable substitute could be found.  I have added descriptive text in places, where before there were bare lists of indices.  One further question: why is G included as a symmetry of group 7, but not of group 3?  It seems to me that it should either be included in both, or omitted from both.  I have a preference for the latter, since, if my understanding is correct, the G in these cases is the composition of T and H. Will Orrick (talk) 09:24, 12 December 2015 (UTC)

text: Regarding the listing of G in groups 3 and 7, some additional thinking has brought me around to the opposite point of view, namely that G ought to be listed for both.  It seems better to list all of the symmetries for each group, even when some are compositions of others.  For some examples: T is listed in group 2, even though it is the composition of two Gs; R is listed in group 7, even thought it is a composition of H and V.  Moreover, while it is true that the G in groups 3 and 7 is the composition of T and H, it is equally true that T is the composition of G and H in these groups.  The discussion of possible minimal sets of generators is a separate one that is already done very well in the article.  It seems that the removal of G from group 3 was only done in 2014.  I'm going to go ahead and add G back, both in the template and in the summary table.  I will include a remark that it arises as the composition of T and H. Will Orrick (talk) 13:39, 13 December 2015 (UTC)
thread_title:  numbering of groups 

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thread_title:  External links modified