Talk:Perles configuration

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Wikipedia

GA review

This review is transcluded from Talk:Perles configuration/GA1. The edit link for this section can be used to add comments to the review.

Nominator: David Eppstein (talk · contribs) 06:11, 28 October 2025 (UTC)

Reviewer: Alex26337 (talk · contribs) 19:58, 3 February 2026 (UTC)


Hello, I've decided to take the time and review this article. Please be patient, as I pace myself and provide any issues within the table below. — Alex26337 (talk) 19:58, 3 February 2026 (UTC)

Information Note: I reformatted the references in preparation for this review. I hope that is not a problem though; even though I never touched the prose itself while doing this, I accidentally occured 30% of the article's authorship. I'll still review the article, and when all is said and done, I'll ask the community to see if my review still validates.

While I am reviewing, I may ask about which page or section the references are verified under, if they prove to be too complicated. If it comes to this, it will be up to you to format the citations to point to the appropriate pages and sections (if you have any questions on how to properly do this, feel free to ask, and I can show you a way). — Alex26337 (talk) 04:20, 4 February 2026 (UTC)

I reverted your change to the reference format per WP:CITEVAR. There is nothing in the GA rules that requires any specific reference format nor even a consistent reference format. See also Wikipedia:Good article criteria footnote [4]. There is also nothing in our citation formatting guidelines (which are not part of the GA rules) discouraging short footnotes. And you also changed some article text that was not a reference, giving credit to certain researchers for their contributions; that is not about citation formatting at all. Please do not do any of those things again. —David Eppstein (talk) 07:05, 4 February 2026 (UTC)
@David Eppstein: Okay, I understand that I should of asked you before I did those edits, but I'm confused as to how (or I guess, where), my edits effected the prose of the article? I did try my best to preserve the information already on the prose, and add information to the references, without altering the direction of the references themselves, or moving them in any way around the article (aside from the end of the section).
I guess one thing that worried me was whether the appropriate references could be pinpointed correctly (since there are some that prove to be very long). In fact, now that I'm saying this, I probably shouldn't have added those page numbers without going over it with you first. Okay, I'm going to try and start over my thought process here, but I still want to know what you think about how I tried (and am trying) to approach this (even though it ended up being inconsiderate)? — Alex26337 (talk) 07:17, 4 February 2026 (UTC)
According to CITEVAR, if the references are consistently formatted (as they are: short footnotes and longer references later, pretty much as recommended in WP:CITESHORT) then you should not change that format to something else (mostly long footnotes but a few short with their full references later) without a talk-page discussion reaching a consensus to do so.
Regarding page numbers, all book references already include page numbers for the relevant (and often relatively short) parts of the book. All journal article references include page numbers for the full journal article, as the full journal article citation format dictates. But one advantage of the current citation format, with separate short and long citations, is that it would be easy to add more specific page numbers to the short citations, if there is a need for that. You might notice, for instance, that the Chaplick et al. reference already does that, picking out 5 specific pages of a 29-page journal article.
As for changing the article text, there turns out to be less of that than I thought; you seem to have left the embedded harv templates alone. However, you did break at least one link from a short call-out in the article text to Mac Lane 1936 by changing the surname of Saunders Mac Lane to "Maclane". You also changed Cardinal & Hoffmann from 2017 to 2016; I think that was a mistake. 2016 is listed as when the paper actually appeared on the journal web site, but the official publication date (the date given for that issue of the journal, as listed on the journal landing page, arXiv, and MathSciNet) is 2017. —David Eppstein (talk) 07:37, 4 February 2026 (UTC)
@Alex26337: Anyway, I hope that formatting issue hasn't derailed the rest of the GA review; I am ready and willing to listen to any substantive suggestions you may have on the article content, sourcing, etc. —David Eppstein (talk) 00:52, 9 February 2026 (UTC)
Rate Attribute Review Comment
1. Well-written:
1a. the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct. "Project invariance and irrationality", paragraph (¶) 1
  • "...specifying in terms of these coordinates the position..." → "...specifying, in terms of these coordinates, the position..." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Because this sentence already had a comma separating two independent clauses, I didn't think adding more commas signifying less-significant pauses was a good idea. To avoid this problem, I split it into two shorter sentences.
    Incidentally, the title of this section uses the word "Projective"; "Project" is incorrect. —David Eppstein (talk) 01:58, 23 February 2026 (UTC)
  • "...collinearity of the points constrains it to obey a quadratic equation, the equation satisfied by the golden ratio." → "...collinearity of the points constrains it to obey a quadratic equation satisfying the golden ratio." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    This suggestion is not an improvement because its use of the indefinite article suggests that there are multiple quadratics that are satisfied by the quadratic equation and that we are somehow picking one of them (but not telling the reader which one). Also it reverses subject and object: a value satisfies an equation, not vice versa. But again, this suggestion led me to notice a too-long sentence, which I have split up, eliminating the issue with the repeated word. —David Eppstein (talk) 01:58, 23 February 2026 (UTC)

"Project invariance and irrationality" ¶ 2

Major issues
  • "...every realization has four points having the same cross-ratio as the cross-ratio of the four collinear points in the realization derived from the regular pentagon.": This part of the sentence presents itself in a redundant, reflective form. Do you think you can change "having" to "with", and rewrite the sentence starting from "as" so that it doesn't seem so repetitive? — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Rewritten, but it was not redundant. In mathematical notation, for all realizations R, and the pentagonal realization P, cr(R)=cr(P). We are saying that two cross-ratios are equal so if phrasing the same thing in English rather than in notation we need to say "cross-ratio" twice to refer to them. —David Eppstein (talk) 01:58, 23 February 2026 (UTC)
Grammatic Issues
  • "But, these four points..." → "However, these four points..." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Eliminated as part of the rewrite above. —David Eppstein (talk) 01:58, 23 February 2026 (UTC)

"Applications § In polyhedral combinatorics" ¶ 1

  • "Perles used his configuration to construct an eight-dimensional convex polytope with twelve vertices that can similarly be realized with real coordinates but not with rational coordinates.[4] It is called the Perles polytope.[5]" → "Perles used his configuration to construct the Perles polytope, an eight-dimensional convex polytope with twelve vertices that can similarly be realized with real coordinates but not with rational coordinates.[4][5]": The term "Perles polytope" should be italicized and delinked. — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Ok, but I left the reference for the Perles polytope name attached to the name rather than floating it to the end of the paragraph. —David Eppstein (talk) 02:35, 23 February 2026 (UTC)

"Applications § In discrete geometry" ¶ 1

  • "...a 2021 conjecture of M. Mirzaei and A. Suk,..." → "...a 2021 conjecture of Mozhgan Mirzaei and Andrew Suk,...": These are the full names of the authors, as referred to in this reference. — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Done. Also I'm a little surprised that Suk doesn't have an article after his 2016 breakthrough on the happy ending problem but I guess that hasn't translated into notability that would be visible in Wikipedia terms. —David Eppstein (talk) 08:13, 23 February 2026 (UTC)
  • "...when the forbidden configuration is an irrational configuration,..." → "...when the forbidden configuration is irrational,..." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    I can see why you would want to avoid the configuration...configuration repetition, but that phrasing would be awkward with the following clause "such as the Perles configuration". I rephrased it in a different way.

"Applications § In discrete geometry" ¶ 2

  • "Cardinal & Hoffmann (2017) showed how to convert problems..." → "Jean Cardinal & Udo Hoffmann showed how to convert problems..." (see this discussion on the deprecation of inline citational parenthesis) — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Sadly, you seem to have caught the virus from A.Cython. That discussion was about citations. The text you are objecting to is article text, not a citation. You can tell because it is grammatically part of the sentence it belongs to; removing it and leaving the remaining wording unchanged would leave an ungrammatical sentence without its subject. the citations are in a different format, and had I for some strange reason wanted to use the deprecated parenthetical format they would still be in a different format, like "(Cardinal & Hoffman 2017)" rather than "Cardinal & Hoffman (2017)". The deprecation of certain citation formats is not about text style and cannot affect text style. Perhaps that style of text is too telegraphic and it should be spelled out that the number is a year by saying "in 2017" rather than "(2017)". Perhaps the year is unimportant and should be omitted. Perhaps the in-text wikilink to the actual reference is too distracting and should be omitted, forcing readers who want to find it to look for the footnote reference instead. But this is not a reference and is not deprecated. In any case, this was reformatted by another editor before you left this comment. —David Eppstein (talk) 03:34, 23 February 2026 (UTC)

"Applications § Other"

  • I feel like it is better to title this section as "Other applications" rather than just the one word. — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    Here the Wikipedia Manual of Style disagrees with you. MOS:NOBACKREF: "section headings should not...refer to a higher-level heading, unless doing so is shorter or clearer". —David Eppstein (talk) 08:05, 23 February 2026 (UTC)

"Applications § Other" ¶ 2

  • "...before the removal of one of these lines to form the Perles configuration." → "...before the removal of one of these lines forms the Perles configuration." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)

"History and related work" ¶ 1

  • "It is not the first known example of an irrational configuration of points and lines. Mac Lane (1936) describes an 11-point example,..." → "It is not the first known example of an irrational configuration of points and lines; Saunders Mac Lane describes an 11-point example,..." (see this discussion on the deprecation of inline citational parenthesis) — Alex26337 (talk) 08:31, 20 February 2026 (UTC)

"History and related work" ¶ 2

  • "There is a long history of study of regular projective configurations,..." → "There is a long history of the study of regular projective configurations,..." — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
  • "Not every abstractly-described system of points and lines has a planar realization; the Möbius–Kantor configuration of eight points and eight lines does not.": While the first part of the sentence (before the semicolon) is fine, and the facts are fine as well, I believe the second part of the sentence should be reworded, because currently, the sentence is written as if there is a list of non-realization-including items, when there is only one (i.e., the fact on Kantor's configuration). While I do have my internal suggestions on this, do you think you can rewrite the second part of the sentence without the semicolon? — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
    See Colon (punctuation) § Usage in English: You are thinking of the "Colon used before list" usage, but here it is a different usage, "Colon before explanation". The part after the colon explains why not every such system has a realization: because there exists (at least) one that does not, and more specifically because the Möbius–Kantor configuration does not. But your comment here did turn up a punctuation issue: it was actually a semicolon and should have been a colon. —David Eppstein (talk) 08:20, 23 February 2026 (UTC)
1b. it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation.
2. Verifiable with no original research, as shown by a source spot-check:
2a. it contains a list of all references (sources of information), presented in accordance with the layout style guideline.
  • I've been reading the information you provided from the WP:CITEVAR and WP:CITESHORT pages, and while there is a consistency and proper layout shown in the lists of citations, I don't think its a good idea to leave the page number out for the shorthand footnotes. I understand that it is better to exclude page ranges that represent every page from the reference due to the range being redundant, but if there is specific information from the sentence the citation refers that is clearly identified on a certain page from it, then that page (or pages) should be marked as such on the shorthand footnote. Otherwise, it would be better to just include the full citation right beside the sentence, instead of using a shorthand footnote to link to it. — Alex26337 (talk) 11:11, 12 February 2026 (UTC)
2b. reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose).

(Information Reviewer's Note: The reference numbers refer to this revision of the article.)

  • Ref. #3c: I do not see this citation referencing or containing information on the Möbius–Kantor configuration, the maximum arrangement containing 13 points, or Grünbaum's conjecture with the Euclidean realization. Do you think you can help by directing me to which sections in the citation the information is located in, or provide a more adequate reference (or references) to validate this information? (Note: I'm referring to the DOI version of this citation, and NOT the arXiv prepublication.) — Alex26337 (talk) 08:41, 15 February 2026 (UTC)
    Green checkmarkY Resolved by the nominator: I had to understand the notations of geometric configurations to get the message, so thanks for pointing it out for me! — Alex26337 (talk) 11:44, 18 February 2026 (UTC)
  • Ref. #4a: On this reference's page, I am unsure where it states that the points are "doubled and with positive, negative, or zero signs assigned to each". — Alex26337 (talk) 11:11, 12 February 2026 (UTC)
    Gray equals sign= Response to nominator's edit: I can see the associated signs being connected to the diagram, though I am skeptical on "zero signs" being added. I guess if the point itself were to equal zero, then it could stick to such a terminology. Alright, I don't think I need to worry about this particular issue, however there is one more thing bothering me: where is the term "Perles polytope" even mentioned in the reference? I get that polytopes referring to Perle's configuration have been mentioned in the citation, but I don't see any explicit mention that it is referred to through this nomenclature. — Alex26337 (talk) 11:44, 18 February 2026 (UTC)
    It turns out that the Grünbaum reference doesn't use exactly that name; instead it says things like "Perles' example of a non-rational 8-polytope with 12 vertices". I added another reference for the name. (It's in the abstract of the cited paper.) —David Eppstein (talk) 18:36, 18 February 2026 (UTC)
    Also, re the "zero signs" see Gale diagram#Affine diagram. It is a notational convention that has nothing to do with the coordinates of the points. Instead of positive/negative/zero, the linked article suggests using colors black/white/grey; it would mean the same thing. —David Eppstein (talk) 20:12, 18 February 2026 (UTC)
    Green checkmarkY Like I said, I can kind-of see the context of "zero signs", so at a minimum, it is fine, and thanks for adding that additional reference. — Alex26337 (talk) 08:31, 20 February 2026 (UTC)
  • Ref. #4b: I don't see any direct mention of Steinitz's theorem on this page. Is there another page in this citation that can refer to and connect the information presented? — Alex26337 (talk) 11:11, 12 February 2026 (UTC)
    Green checkmarkY Resolved by the nominator: Thanks for redirecting the citation to a page number that can work. — Alex26337 (talk) 11:44, 18 February 2026 (UTC)
  • Ref. #6: The term "Perles matroid" does not seem to be directly referenced in the citation. Also, while I was able to find bits and pieces of what was mentioned in this paragraph, such as how finite fields are defined in the reference, it's difficult for me to pinpoint where in the citation this information is explicitly stated. Do you think you can help direct me to which lemmas, proofs, or theorems contain what's stated in each sentence that citation is referring to (you can just mention their section numbers)? I feel like the majority of it is between Lemma 14.3 and 14.8, but again, I am unsure as to how much, or if its better explained in another area of the citation. Also, I know that the information won't be exactly worded as what's presented in the article, but it would nonetheless be helpful to know where it's mentioned. — Alex26337 (talk) 21:09, 12 February 2026 (UTC)
    Gray equals sign= Respone to nominator's edit: The reference does provide evidence for the term "Perles matroid", however, I think it's better if you move the new reference (i.e. Ref. #8') right at the end of the first sentence of its paragraph. This is because The information on the second sentence is supported in ref. #9', but not in ref. #8'. — Alex26337 (talk) 11:44, 18 February 2026 (UTC)
     Done Ok, moved. —David Eppstein (talk) 18:28, 18 February 2026 (UTC)
2c. it contains no original research.
2d. it contains no copyright violations or plagiarism.
3. Broad in its coverage:
3a. it addresses the main aspects of the topic.
3b. it stays focused on the topic without going into unnecessary detail (see summary style).
4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each.
5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute.
6. Illustrated, if possible, by media such as images, video, or audio:
6a. media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content.
  • There is only one image in this article, and it has been released by its creator under a CC Zero 1.0 license. No issues with this sub-criteria: Pass
6b. media are relevant to the topic, and have suitable captions.
  • The only image on this page and its caption has proven to be relevant and is explained in the prose. No further issues here: Pass
7. Overall assessment.

Thanks! Some responses to your comments:

Re criterion 2a: All citations already contain a range of relevant pages (for book citations) or the entire range of publication pages (for journal pages), exactly the information that the citation templates provide for. The fact that this is primarily formatted with the pages as part of the long citation and without the page numbers being repeated in the short citation should be irrelevant. Again, see Wikipedia:Good article criteria, footnote 4 to criterion 2a: "Using consistent formatting or including every element of the bibliographic material is not required". However, in cases where it may be helpful, additional specificity in page numbers could be added to the short descriptions, although I do not think the GA criteria require it. And with some of the responses below I have added this information.

Re criterion 2b, ref #3c (Solymosi): for the Möbius–Kantor configuration (by description but not by name) see page 915, first bullet, first sub-bullet, "It is the unique 8_3 configuration, which is realizable over the complex numbers but not over the reals". Re "at most 13 points" and Grünbaum's conjecture: see discussion at the end of section 1, page 913, "Conjecture 1 (Grünbaum)", Theorem 1 of Strumfeld and White on all n_3 configurations with at most 12 points, and the line following conjecture 1 stating "The case 13_3 was recently proved by Kocay". I split this footnote into two footnotes with these page numbers.

Ref 4a (Grünbaum): This was an incorrect page numbering, now corrected. The correct pages were 94–95, not 96a. The text about doubling and signs is intended as a simplified description of the formula at the top of p95.

Ref 4b (Grünbaum, now 5): I agree that the citation only covered the part of this sentence after the reference to Steinitz's theorem. I added a reference to page 244 of the same book (noting that the theorem 13.1.1 referred to on that page is in fact Steinitz's theorem). I also reworded it because it was not clear to me whether the proof described in this source is actually Steinitz's original proof and I don't think that was an important point.

Ref 6 Grace, now 8): I added another reference (Corey 2021) for the "Perles matroid" name. By the way, this illustrates the limitations of demanding page numbers within article references: The pdf journal version of Corey 2021 has different figure numbers and a different pagination than the arXiv version, making it complicated to tell readers exactly where to look. The html journal version has no page numbers at all. As for where material appears in Grace 2021: the journal version timed out for me so I had to refer to the arXiv version for which the pagination and maybe the theorem numbering are not the same. The matroid in question is called Y9 in this reference; its dual is Y9*. "applied in characterizing certain classes of matroids": Theorem 1.5 and Theorem 1.6, pp.2-3 of the arXiv version. "Linear over F4" is implicit throughout but described explicitly (for the closely related "Betsy Ross matroid" from which the same result for the Perles matroid is immediate) on p.67. Not rational: See the proof of Lemma 14.7, p. 71. In these cases I did not add page numbers to the footnotes because of the problem with the journal web site.

—David Eppstein (talk) 00:53, 17 February 2026 (UTC)

Thanks for your help; I added new comments in the box accordingly. Feel free to comment inside it or under this comment with any feedback! — Alex26337 (talk) 11:44, 18 February 2026 (UTC)

Magenta clockclock Okay, I'm pretty much done with my inital review. All the references have been verified; it's just the prose itself that remains. I know that these issues will most likely be done very soon, but I'm still just going to procedurally put this on a 7-day hold anyways. Once everything is taken care of, I'll do my final review. Thanks for being patient with me. — Alex26337 (talk) 08:31, 20 February 2026 (UTC)