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"By way of example, the space group of quartz is P3121,..."
"In the international short symbol the first symbol (31 in this example) denotes the symmetry along the major axis "
This makes no sense at all. Surely "P" is the first symbol. If P isn't being counted as a symbol, then what exactly do we mean by a symbol? I'm trying to gain some understanding of this topic, and this article (like so many others on the subject) seems incomprehensible, to such as extend that even some of the most basic terms like "symbol" seem to be being used in a unconventional way with no explanation of their meaning in this context. — Preceding unsigned comment added by 95.131.110.106 ( talk) 11:09, 18 February 2014 (UTC)
How can I mark this page as 'needs to be clearer for a lay person'? Its good, but some of the english seems to be wrong, and not being an expert I am not able to fix it...
"with a threefold screw axis projecting on one face, and two fold rotation axis another."
Is this simply
"with a threefold screw axis projecting on one face, and two fold rotation axis on another."
?
It isn't clear where this information comes from given the space group.
-- Dan| (talk) 17:15, 25 July 2005 (UTC)
I've added the attention tag to this article. I believe the article is factually correct, but it is very unclear to me (and I have some knowledge on the subject). To a lay-person it would be completely unreadable. I might get around to doing something about it myself, but I'm sure there are more qualified people out there. If I do it, I might miss out on some of the mathematics. (actually I'm quite sure I would) O. Prytz 15:49, 26 December 2005 (UTC)
This article makes no mention of the symmetry operation x y z = -x -y -z, called an "inversion center" or "center of symmetry". While it could be considered a subset of improper rotation (rotoinversion rather than rotoreflection, in this case) it is usually classed by itself. The presence (or absence) of an inversion center is an important way to classify space groups in X-ray crystallography for a couple of reasons. The article would be much improved by at least mentioning this. M.Dickman 09:07, 14 August 2007 (UTC)
I've brought back some old text and put it at the start of the article under the heading 'Space groups in crystallography'. All the text from the previous version is still there, but I've put it under the heading 'Group theory'. I don't propose keeping things exactly as they are now, but Patrick: what do you think of structuring the article along these lines? O. Prytz 07:48, 2 January 2006 (UTC)
Good! I belive this arrangement will work. I also agree with most of the changes you've made to the beginning of the article, but I'll probably make some small changes eventually. O. Prytz 18:45, 2 January 2006 (UTC)
Ok, I've had a look at the first part of the article and want to suggest some changes. I haven't made the changes to the article itself yet, but rather copied the text here and edited that copy. I've added sections and rewritten a little bit. Regarding notation: the old version stated that two types of notation are used: the Paterson notation and Schönflies. I believe it should be Hermann-Mauguin and Schönflies. I haven't found refrences supporting the name "Paterson notation", although I don't have the International Tables in front of me. Other than that, I've only corrected an error in the description of glide planes. What do you think? O. Prytz 20:19, 4 January 2006 (UTC)
I've created the articles Screw axis and Glide plane using some of the text from this article. These articles are stubs and should be expanded somewhat so please go ahead. I hope they don't need to get too mathematical, we should at least keep an introductory text at the level of the current text.
As a follow up, I've removed the screw axis and glide plane paragraphs in the group theory section of this article. Hope that's ok. Patrick: would it be at all possible to shorten the group theory text any further, and instead refer to another article? O. Prytz 12:08, 8 January 2006 (UTC)
There are a number of other articles (and redirects) which to me seem to confuse various topics related to crystal symmetry. Here are some examples:
I'll probably start editing several of these articles, so this is a heads up to anyone wanting to follow up and check the changes I make. I'll do my best to check all changes with the Iternational tables of crystallography and other sources, but there's bound to be some inaccuracies in the things I do. O. Prytz 16:37, 8 January 2006 (UTC)
I removed the attention tag as I think the article has gotten a lot better. Some work is still needed though. What do you guys think? O. Prytz 07:28, 10 January 2006 (UTC)
there are almost 230 unique space groups describing all possible crystal symmetries. but when it comes to protein crystallography why there are only 32 space groups considered??? —Preceding unsigned comment added by Intelligeno ( talk • contribs) 08:49, August 30, 2007 (UTC)
اناميسي من ليبيا احب بشلونة واتمنا لسبيستون النجاحوالتوفيق واتمنا الفوز لبرشلونة امام هرنان —Preceding unsigned comment added by 41.252.5.62 ( talk) 21:57, 9 July 2008 (UTC)
"A definitive source regarding 3-dimensional space groups is Hahn (2002)."
Is it appropriate to recommend a textbook in the lead? I haven't seen another article have such a line in its lead; it almost seems like an advertisement. Is there any objection to me removing it? JHobbs103 ( talk) 22:03, 29 May 2010 (UTC)
I'm considering adding to that table how many:
I propose this explanation of the difference between arithmetic and geometric crystal classes: A geometric crystal class is for a point group considered in isolation, while an arithmetic crystal class is for a point group with some orientation relative to the lattice. The distinction between arithmetic and geometric crystal classes is easier to visualize in two dimensions, in the wallpaper groups. I'll list them by geometric crystal class (point group), with arithmetic crystal classes in sublists:
A problem with adding these statistics is the headers -- they would grow even larger than they are now. I am thinking of using abbreviations and moving the full headers to a list below the table. That list may itself be a table, with links to the Online Encyclopedia of Integer Sequences and the like. — Preceding unsigned comment added by Lpetrich ( talk • contribs) 21:05, 6 January 2013 (UTC)
Done both. For the small-dimension table, I turned most of the column headers into abbreviations, because the full text makes them too wide. IMO, the resulting table is much cleaner-looking, even though it has more columns.
I have found a problem, however. Discrepancies between various published and stated values in the numbers, especially for 6 dimensions. Could someone with good journal access please review the literature on the subject of these numbers? Some of the relevant articles are paywalled.
Lpetrich ( talk) 15:24, 9 January 2013 (UTC)
In the interest of clarity, it would be helpful to pick a single transliteration of Фёдоров, at least with respect to the internal consistency of the article. There are several reasons to use Fyodorov instead of Fedorov:
In summary, Fedorov lacks internal consistency within Wikipedia and is by far the rarer spelling.
99.196.225.79 ( talk) 03:39, 1 May 2013 (UTC)
Bor75 ( talk) 06:37, 1 May 2013 (UTC)
I compiled a list of space groups with their full names, with spaces for readability, replacing redirect at list of space groups. Tom Ruen ( talk) 23:17, 10 February 2014 (UTC)
I think the introdution should change to
"
In mathematics and physics, a space group is the symmetry group of a configuration in space, usually in three dimensions. A symmetry group of R3 belongs to a space group iff the subgroup of all translations in that group is generated by 3 linearly independent translations and the symmetry group has only finitely many cosets of the subgroup of all translations in it. Two symmetry groups that belong to a space group belong to the same space group iff there exists a linear transformation R such that the function that assigns to each transformation T in the first symmetry group R-1TR is a bijection from the first symmetry group to the second symmetry group. Note that R-1TR doesn't necessarily have to be an isometry for all isometries T; it just has to be an isometry for all symmetry operations T of the first symmetry group. In total there are 219 such symmetry groups. For each space group, either all structures that belong to that space group are chiral or none of them are. Some authors consider chiral copies of a space group to be distinct, that is, there define a space group pretty much the same way except for replacing the criterion "there exists a linear transformation R such that" with "there exists a non-inverting linear transformation R such that". 11 of the members of the first definition of a space group can be split into 2 members of the second definition leaving a total of 230 space groups according to the second definition. Those 11 space groups are called chiral space groups. Although all structures that belong to a chiral space group are chiral structures, not all chiral structures that belong to a space group belong to a chiral space group. Space groups are also studied in dimensions other than 3 where they are sometimes called Bieberbach groups, and are discrete cocompact groups of isometries of an oriented Euclidean space.
In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography ( Hahn (2002) )." to better explain what a space group is.
Can anyone find sources for any of the information I added? Blackbombchu ( talk) 01:17, 24 November 2014 (UTC)
Comparing the definition of "group" in the context of this article to the mathematical definition of a group, the requirements of "space groups" are stated as properties of certain "group actions" of mathematical groups. For readers only familiar with the properties of a mathematical group, it would helpful to point out that term "group" in this article may often refer to what mathematicians call a "group action". — Preceding unsigned comment added by Tashiro ( talk • contribs) 15:55, 13 February 2015 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
"By way of example, the space group of quartz is P3121,..."
"In the international short symbol the first symbol (31 in this example) denotes the symmetry along the major axis "
This makes no sense at all. Surely "P" is the first symbol. If P isn't being counted as a symbol, then what exactly do we mean by a symbol? I'm trying to gain some understanding of this topic, and this article (like so many others on the subject) seems incomprehensible, to such as extend that even some of the most basic terms like "symbol" seem to be being used in a unconventional way with no explanation of their meaning in this context. — Preceding unsigned comment added by 95.131.110.106 ( talk) 11:09, 18 February 2014 (UTC)
How can I mark this page as 'needs to be clearer for a lay person'? Its good, but some of the english seems to be wrong, and not being an expert I am not able to fix it...
"with a threefold screw axis projecting on one face, and two fold rotation axis another."
Is this simply
"with a threefold screw axis projecting on one face, and two fold rotation axis on another."
?
It isn't clear where this information comes from given the space group.
-- Dan| (talk) 17:15, 25 July 2005 (UTC)
I've added the attention tag to this article. I believe the article is factually correct, but it is very unclear to me (and I have some knowledge on the subject). To a lay-person it would be completely unreadable. I might get around to doing something about it myself, but I'm sure there are more qualified people out there. If I do it, I might miss out on some of the mathematics. (actually I'm quite sure I would) O. Prytz 15:49, 26 December 2005 (UTC)
This article makes no mention of the symmetry operation x y z = -x -y -z, called an "inversion center" or "center of symmetry". While it could be considered a subset of improper rotation (rotoinversion rather than rotoreflection, in this case) it is usually classed by itself. The presence (or absence) of an inversion center is an important way to classify space groups in X-ray crystallography for a couple of reasons. The article would be much improved by at least mentioning this. M.Dickman 09:07, 14 August 2007 (UTC)
I've brought back some old text and put it at the start of the article under the heading 'Space groups in crystallography'. All the text from the previous version is still there, but I've put it under the heading 'Group theory'. I don't propose keeping things exactly as they are now, but Patrick: what do you think of structuring the article along these lines? O. Prytz 07:48, 2 January 2006 (UTC)
Good! I belive this arrangement will work. I also agree with most of the changes you've made to the beginning of the article, but I'll probably make some small changes eventually. O. Prytz 18:45, 2 January 2006 (UTC)
Ok, I've had a look at the first part of the article and want to suggest some changes. I haven't made the changes to the article itself yet, but rather copied the text here and edited that copy. I've added sections and rewritten a little bit. Regarding notation: the old version stated that two types of notation are used: the Paterson notation and Schönflies. I believe it should be Hermann-Mauguin and Schönflies. I haven't found refrences supporting the name "Paterson notation", although I don't have the International Tables in front of me. Other than that, I've only corrected an error in the description of glide planes. What do you think? O. Prytz 20:19, 4 January 2006 (UTC)
I've created the articles Screw axis and Glide plane using some of the text from this article. These articles are stubs and should be expanded somewhat so please go ahead. I hope they don't need to get too mathematical, we should at least keep an introductory text at the level of the current text.
As a follow up, I've removed the screw axis and glide plane paragraphs in the group theory section of this article. Hope that's ok. Patrick: would it be at all possible to shorten the group theory text any further, and instead refer to another article? O. Prytz 12:08, 8 January 2006 (UTC)
There are a number of other articles (and redirects) which to me seem to confuse various topics related to crystal symmetry. Here are some examples:
I'll probably start editing several of these articles, so this is a heads up to anyone wanting to follow up and check the changes I make. I'll do my best to check all changes with the Iternational tables of crystallography and other sources, but there's bound to be some inaccuracies in the things I do. O. Prytz 16:37, 8 January 2006 (UTC)
I removed the attention tag as I think the article has gotten a lot better. Some work is still needed though. What do you guys think? O. Prytz 07:28, 10 January 2006 (UTC)
there are almost 230 unique space groups describing all possible crystal symmetries. but when it comes to protein crystallography why there are only 32 space groups considered??? —Preceding unsigned comment added by Intelligeno ( talk • contribs) 08:49, August 30, 2007 (UTC)
اناميسي من ليبيا احب بشلونة واتمنا لسبيستون النجاحوالتوفيق واتمنا الفوز لبرشلونة امام هرنان —Preceding unsigned comment added by 41.252.5.62 ( talk) 21:57, 9 July 2008 (UTC)
"A definitive source regarding 3-dimensional space groups is Hahn (2002)."
Is it appropriate to recommend a textbook in the lead? I haven't seen another article have such a line in its lead; it almost seems like an advertisement. Is there any objection to me removing it? JHobbs103 ( talk) 22:03, 29 May 2010 (UTC)
I'm considering adding to that table how many:
I propose this explanation of the difference between arithmetic and geometric crystal classes: A geometric crystal class is for a point group considered in isolation, while an arithmetic crystal class is for a point group with some orientation relative to the lattice. The distinction between arithmetic and geometric crystal classes is easier to visualize in two dimensions, in the wallpaper groups. I'll list them by geometric crystal class (point group), with arithmetic crystal classes in sublists:
A problem with adding these statistics is the headers -- they would grow even larger than they are now. I am thinking of using abbreviations and moving the full headers to a list below the table. That list may itself be a table, with links to the Online Encyclopedia of Integer Sequences and the like. — Preceding unsigned comment added by Lpetrich ( talk • contribs) 21:05, 6 January 2013 (UTC)
Done both. For the small-dimension table, I turned most of the column headers into abbreviations, because the full text makes them too wide. IMO, the resulting table is much cleaner-looking, even though it has more columns.
I have found a problem, however. Discrepancies between various published and stated values in the numbers, especially for 6 dimensions. Could someone with good journal access please review the literature on the subject of these numbers? Some of the relevant articles are paywalled.
Lpetrich ( talk) 15:24, 9 January 2013 (UTC)
In the interest of clarity, it would be helpful to pick a single transliteration of Фёдоров, at least with respect to the internal consistency of the article. There are several reasons to use Fyodorov instead of Fedorov:
In summary, Fedorov lacks internal consistency within Wikipedia and is by far the rarer spelling.
99.196.225.79 ( talk) 03:39, 1 May 2013 (UTC)
Bor75 ( talk) 06:37, 1 May 2013 (UTC)
I compiled a list of space groups with their full names, with spaces for readability, replacing redirect at list of space groups. Tom Ruen ( talk) 23:17, 10 February 2014 (UTC)
I think the introdution should change to
"
In mathematics and physics, a space group is the symmetry group of a configuration in space, usually in three dimensions. A symmetry group of R3 belongs to a space group iff the subgroup of all translations in that group is generated by 3 linearly independent translations and the symmetry group has only finitely many cosets of the subgroup of all translations in it. Two symmetry groups that belong to a space group belong to the same space group iff there exists a linear transformation R such that the function that assigns to each transformation T in the first symmetry group R-1TR is a bijection from the first symmetry group to the second symmetry group. Note that R-1TR doesn't necessarily have to be an isometry for all isometries T; it just has to be an isometry for all symmetry operations T of the first symmetry group. In total there are 219 such symmetry groups. For each space group, either all structures that belong to that space group are chiral or none of them are. Some authors consider chiral copies of a space group to be distinct, that is, there define a space group pretty much the same way except for replacing the criterion "there exists a linear transformation R such that" with "there exists a non-inverting linear transformation R such that". 11 of the members of the first definition of a space group can be split into 2 members of the second definition leaving a total of 230 space groups according to the second definition. Those 11 space groups are called chiral space groups. Although all structures that belong to a chiral space group are chiral structures, not all chiral structures that belong to a space group belong to a chiral space group. Space groups are also studied in dimensions other than 3 where they are sometimes called Bieberbach groups, and are discrete cocompact groups of isometries of an oriented Euclidean space.
In crystallography, space groups are also called the crystallographic or Fedorov groups, and represent a description of the symmetry of the crystal. A definitive source regarding 3-dimensional space groups is the International Tables for Crystallography ( Hahn (2002) )." to better explain what a space group is.
Can anyone find sources for any of the information I added? Blackbombchu ( talk) 01:17, 24 November 2014 (UTC)
Comparing the definition of "group" in the context of this article to the mathematical definition of a group, the requirements of "space groups" are stated as properties of certain "group actions" of mathematical groups. For readers only familiar with the properties of a mathematical group, it would helpful to point out that term "group" in this article may often refer to what mathematicians call a "group action". — Preceding unsigned comment added by Tashiro ( talk • contribs) 15:55, 13 February 2015 (UTC)