User talk:Dc.samizdat

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Jitterbug

Thank you for your edit to the disambiguation page Jitterbug (disambiguation). However, please note that disambiguation pages are not articles; rather, they are meant to help readers find a specific article quickly and easily. From the disambiguation dos and don'ts, you should:

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Thank you.

I don't disagree with your addition to Jitterbug (disambiguation), but it needs to be discussed in an existing article before it is added to a disambiguation page. I couldn't find 'Jitterbug' in either Buckminster Fuller or Jessen's icosahedron (except in a reference title). If you'd like to add the information to one of these articles, then it could go back on the disambiguation page. Leschnei (talk) 18:21, 23 February 2019 (UTC)

600-cell

Welcome to Wikipedia. We appreciate your contributions, but in one of your recent edits to 600-cell, it appears that you have added original research, which is against Wikipedia's policies. Original research refers to material—such as facts, allegations, ideas, and personal experiences—for which no reliable, published sources exist; it also encompasses combining published sources in a way to imply something that none of them explicitly say. Please be prepared to cite a reliable source for all of your contributions. Thank you. —David Eppstein (talk) 22:32, 10 May 2019 (UTC)

The 20 cell-disjoint 30-cell rings constitute four identical cell-disjoint 150-cell tori: the two described in the grand antiprism decomposition above, and two more that fill the middle layer of 300 tetrahedra between them (which includes the 100 tetrahedra on the Clifford torus boundary).

I don't think the above quote is entirely correct. If the 600 cell can be decomposed into four identical, Clifford parallel, cell-disjoint, 150-cell tori, I do not believe any pair are orthogonal (like in the grand antiprism decomposition). For a symmetric, four fiber, discrete Hopf fibration, the four fibers must occupy mutually similar points on the Hopf sphere, i.e. the points of a tetrahedron. For the grand antiprism decomposition, the two fibers are orthogonal, on opposite poles of the Hopf sphere. There is then no remaining place on the Hopf sphere to place (only) two more similar points. Cloudswrest (talk) 03:54, 12 March 2023 (UTC)

Interesting. You're right of course, there's an error in the way I describe it. The 12 decagons are a fibration. The 20 30-cell rings are a fibration. Or, four completely disjoint 30-cell rings are a fibration. Five 30-cell rings around a decagon are a 150-cell torus. Two completely disjoint 150-cell tori are a fibration in the grand antiprism decomposition. But I see now why the space between the two 150-cell tori of that decomposition cannot be filled by two more 150-cell tori.

But it still seems to me that the 600-cell can be decomposed into four cell-disjoint 150-cell tori, can it not? That will be a different decomposition than the grand antiprism, with no two of the four 150-cell tori in the same positions (having the same cell set) as the two 150-cell tori of the grand antiprism decomposition. But still a discrete Hopf fibration of 12 Clifford parallel decagon fibers, is it not? Seems to me there are four decagons axial to the four 150-cell tori, and a total of 8 other disjoint decagons shared by the four tori, that comprise their combined exposed in-contact surfaces -- 5 of the 8 are the surface of any one 150-cell torus. Am I dreaming? Dc.samizdat (talk) 18:58, 12 March 2023 (UTC)

Maybe I am dreaming, and there is no way to decompose the 600-cell into four 150-cell tori. To save that idea I'd have to correct the article by explaining the difference between these two 150-cell decompositions of the 120-cell (into two and four 150-cell tori respectively) by reference to their Hopf maps, as you did. So, can I do that? A point on the icosahedral map lifts to a great decagon, a triangular face lifts to a 30-cell ring, and a pentagonal pyramid of 5 faces lifts to a 150-cell ring. In the grand antiprism decomposition, two completely disjoint 150-cell rings are lifted from antipodal pentagons, leaving an annular ring of 10 faces between them: a Petrie decagon of 10 triangles. (The Clifford torus boundary must be lifted from the 0-gon axis of this Petrie polygon, the equator of the icosahedron.) But to get a decomposition into four 150-cell rings, the icosahedral map would have to be decomposed into four pentagons, centered at the vertices of an inscribed tetrahedron. And the icosahedron doesn't come apart that way. So I was dreaming. The 600-cell decomposes into 20 30-cell rings, or 2 150-cell rings and 10 30-cell rings, but not into 4 150-cell rings. Dc.samizdat (talk) 20:07, 14 March 2023 (UTC)

Not 4 150-cell rings of this kind, that is: not 5 30-cell rings around one great decagon. Sadoc describes the decomposition of the 600-cell into four tori. It is the same fibration of 12 great decagons and 20 30-cell rings, seen as a fibration of four completely disjoint 30-cell rings with spaces between them, which still encompasses all 12 decagons and all 120 vertices. If we look closely at the spaces between the four disjoint 30-cell rings, we can discern four 150-cell rings of 5 30-cell rings each. But these 150-cell rings do not have 5 30-cell rings around a common decagon axis. Their axis is a 30-cell ring, not a decagon. To construct them, on each of the four completely disjoint 30-cell rings, face-bond three more 30-cell rings to the exterior faces, making four stellated ("bumpy") tori of four 30-cell rings (120 cells) each. Collectively they contain 16 of the 20 30-cell rings: there are still four 30-cell ring "holes" left to fill in the 600-cell. To do that, fill the surface concavities of each 120-cell ring by wrapping a fifth 30-cell ring around its outside, completely orthogonal to the axial 30-cell ring we started with. The result is four 150-cell tori, of 5 30-cell rings each, each having two completely orthogonal 30-cell ring axes, either of which can be seen as either an axis or a circumference: it is both of course.

What does this 150-cell ring lift from, on the icosahedron Hopf map? The four 30-cell rings lift from a star of four icosahedron faces (three faces edge-bonded around one). The fifth 30-cell ring lifts from a fifth face edge-bonded to the star, a sort of "extra flap" like the sixth square flap of a cardboard box before you fold it up into a cube. It does not matter which of the six possible adjacent faces you choose as the flap, but the choice determines the choice for all four 150-cell rings. There are six choices because there are six decagonal fibrations; this is when you fix which fibration you are taking. Dc.samizdat (talk) 18:01, 16 March 2023 (UTC)

Geodesics in the 600 cell.

I think you missed one. The center axis of the 30-tet Boerdijk–Coxeter helix forms a 30-gon, with each segment passing through a tet similarly. This geodesic resides completely in the surface, the segments are not chords. It doesn't touch any edges or vertexes, but it does hit faces. Cloudswrest (talk) 05:14, 14 February 2021 (UTC)

• That's really interesting! I never even considered geodesics that don't hit vertices. The /*Geodesics*/ sections I added to 600-cell and 24-cell are strictly enumerations of all the central polygons through vertices. That enumeration seems complete in the sense that the squares of their edge lengths sum nicely to the square of the number of vertices in the whole polytope. But the geodesic you describe is certainly a noteworthy feature -- how and where do you think it should be described in the article? Perhaps under 'Rotations', as I imagine it must be its own rotational symmetry element (distinct from those of the central polygons I describe) -- but I don't really understand the SO(4) group of rotations (or group theory at all!). Perhaps it could be mentioned in your 'Visualization / Union of two tori' section about the B-C helicies and Hopf fibrations? Or we could add a subsection under /*Geodesics*/ for non-vertex geodesics.
• Here's what I did: The /*Geodesics*/ section now says that there is at least one other geodesic, that does not pass through any vertices; I added your description of it as a footnote containing a link to the /*Union of two tori*/ section.
• This 30-gon vertex-less geodesic reminds me of another remarkable observation about the central axis of the B-C helix made many years ago by the Dutch software engineer and geometry experimenter Gerald de Jong, on a long-extinct email list called Synergetics that mostly featured discussions of Buckminster Fuller memes. That list didn't extend to 4-polytopes; the geometry discussed there was about 3-dimensional objects, as it also tended to be on Magnus Wenninger's Polyhedron email list. I can't find an archived copy of the email list with Gerald's post but as I recall he studied the B-C helix (Fuller called it the tetrahelix) in 3 dimensions and observed that it had no single central axis joining the tetrahedron centers, but rather three parallel central axes that passed through each tetrahedron similarly, hitting two faces near but not at their center, like three holes punched in the face in a small equilateral triangle surrounding the face center. He called the tetrahedra pierced by the three central axes "tetrahedral salt cellars", a wonderfully evocative image and why I have remembered it (correctly, I hope). Joining the centers of the cells through the centers of the faces produces a skew 30-gon which User:Rolfdieter Frank identified in the 600-cell as the Petrie polygon of a 120-cell, the 600-cell's dual. But there is also a single "straight line" central axis of the B-C helix which is of interest (in the 600-cell it is the 30-gon great circle geodesic): conversely to de Jong's parallels, it passes through the center of each face, but it misses the center of each cell.

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Jessen's icosahedron

Your recent editing history at Jessen's icosahedron shows that you are currently engaged in an edit war; that means that you are repeatedly changing content back to how you think it should be, when you have seen that other editors disagree. To resolve the content dispute, please do not revert or change the edits of others when you are reverted. Instead of reverting, please use the talk page to work toward making a version that represents consensus among editors. The best practice at this stage is to discuss, not edit-war. See the bold, revert, discuss cycle for how this is done. If discussions reach an impasse, you can then post a request for help at a relevant noticeboard or seek dispute resolution. In some cases, you may wish to request temporary page protection.

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Also, the you don't the need to put the the before the every the noun, only before "the tensegrity icosahedron". Please consider that this is a Good Article, and the first requirement of Good Articles (WP:GACR #1a) includes competent grammar. And your version of the article STILL does not actually say that the tensegrity icosahedron is a tensegrity structure. It says what it is called (the tensegrity icosahedron), not what it is (a tensegrity structure). So readers are left bewildered at why it might be called that, and what significance this structure could have (it is just a thing with a name, but why?). Please explain how this could possibly be an improvement rather than continuing to edit-war. —David Eppstein (talk) 07:07, 9 April 2022 (UTC)

I have sent you a note about a page you started

Hello, Dc.samizdat

Thank you for creating Kinematics of the cuboctahedron.

User:SunDawn, while examining this page as a part of our page curation process, had the following comments:

Thanks for the article!

To reply, leave a comment here and begin it with {{Re|SunDawn}}. Please remember to sign your reply with ~~~~ .

(Message delivered via the Page Curation tool, on behalf of the reviewer.)

✠ SunDawn ✠ (contact) 08:32, 2 July 2022 (UTC)

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TOC comment

Hello Dc.samizdat,

I read your comment about the new Vector 2022 ToC here and I found it as a particularly relevant and thoughtful one amongst the others. I would like to open a sub-thread about the ToC, as a particularly salient flaw of the new interface design, here: Wikipedia:Requests for comment/Rollback of Vector 2022. Can I cite your comment verbatim? Æo (talk) 14:46, 22 January 2023 (UTC)

of course, thank you for doing that Dc.samizdat (talk) 00:02, 23 January 2023 (UTC)

Thank you, I quoted it here. Æo (talk) 14:01, 23 January 2023 (UTC)

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December 2023

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Heavy use of explanatory footnotes in the 600-cell article

Hi Beland. Thank you for reviewing the 600-cell article, and for your suggestion that the copious footnotes be simplified and improved, and perhaps pulled inline or moved to separate articles. The article does have a great many explanatory footnotes! The Notes section is 3/5 as large as all the rest of the article combined. That is indeed very unusual for a Wikipedia article, even a large article on a complex topic. So as the author of most of those notes, I feel it is incumbent upon me to try to explain why they are there. The heavy use of multiply-linked explanatory footnotes is certainly an outlier in the range of Wikipedia footnoting styles, but I hope to persuade you that in general they are a feature of this article, not a bug. I do agree that many of the concepts they explain deserve a separate Wikipedia article of their own, and I will be working on developing those articles in the future. It would be ideal to group the text of footnotes on the same topic into an article of its own, so the footnote references can be replaced with links.

The reason for the heavily interlinked footnotes is the special nature of the subject matter. This is an article about a 120-vertex object that lives in the fourth dimension, one of the most complex regular geometric objects in nature. It is bafflingly unfamiliar to nearly all human beings, because none of us has ever had the sensory experience of handling a four-dimensional object, and the only way we can visualize one is in our imagination. Even the illustrations in the article (which are excellent, by the way, and almost all the work of other Wikipedia editors than myself) are very hard to understand, because they are only illustrations of three-dimensional shadows and slices of the 600-cell, which is a four-dimensional object. The surface of the 600-cell is a curved three-dimensional space, the way the surface of the earth is a curved two-dimensional space, but even that is hard to illustrate or comprehend, because it is a curved non-Euclidean three-dimensional space, subtly different from the flat Euclidean three-dimensional every-day space we all live in. So to explain to the reader what he is looking at, even with these fine illustrations of parts of the thing, is quite a challenge.

If you read the 600-cell article section by section, line by line, I think you will find that you do not get far -- not through the first section perhaps -- before you encounter a sentence that makes little sense to you, or a term or expression with which you are unfamiliar, even if you are a mathematician (and I am not). That is the reason for all the links and explanatory footnotes in the article. When you read a sentence and you don't quite get it, there is a footnote you can hover your mouse over, and the little post-it note pops up with more information. Hopefully just what you need to have explained, if I have put the right footnote in the right place.

Where the concept or term has a Wikipedia article of its own, or a section of an article of its own, of course I use links in preference over footnotes, but there are hundreds of concepts and distinct mathematical terms required to enable a reader to visualize the fourth dimension, and not all of them have their own Wikipedia article (yet). Even where they do, an explanatory footnote may be needed in addition to the link, in order to explain the meaning of the term in this unique context; believe me, the 600-cell is really unique! Above all, these ideas really can't be explained in isolation. It happens that the 600-cell is the archetype of many of those concepts, one of the few examples, and in some cases the best example, of a known object which expresses those symmetries. The only way I know to learn to visualize the fourth dimension is by studying the regular 4-polytopes as the examples of four dimensional objects. So a high quality article about the 600-cell is really an article explaining the fourth dimension, by way of the 600-cell as an example. An article which merely lists the 600-cell's properties and provides beautiful incomprehensible pictures of it would not be a high quality article. That's what we'd have if we deleted most of the footnotes, or drastically simplified them.

For the same reason that the 600-cell has a very complex geometry, the footnotes themselves have a very complex geometry. Those unfamiliar terms and strange concepts occur again and again in the article, in distinct but related contexts. Whenever I write a note explaining a concept, I look for other places where the concept arises, such as in other notes about related concepts, and I add a reference to the footnote in those places, too, just where the reader is maybe going to need it. Just as an article may have many links to it, an explanatory note is a mini-article which may have many references to it. I hope that I have linked these notes to each other in the proper way, so that the relationships among the concepts and geometric objects is mirrored in the topology of the notes themselves, so the notes can explain the relationships among themselves to the reader. In this case, the body of footnotes itself is a polytope. Not a regular polytope to be sure, and probably of more than four dimensions in some places, but a complex geometric object to be explored. It is entirely up to the reader how to do that exploring. It is up to him whether he clicks on the footnote-within-a-footnote, just as it is up to him whether he clicks on a footnote in the first place. But if he needs to, he can explore the object or concept the footnote is about in depth, reviewing several notes-within-notes before he satisfies himself that he understands the sentence of the article he was reading that stumped him.

So I invite you to do more reviewing of the article and its footnotes, in greater depth if you have the interest and the time. Tell me which footnotes were helpful to you, which were confusing or unhelpful, and which were unnecessary or redundant or badly linked. I want to improve them, and that always means simplifying them, making them more concise and briefer and fewer, wherever I can find a way to do so. You can help me to do that. Tell me if the fourth dimension makes sense to you, with or without the footnotes. Tell me where you need another footnote to explain something that is not yet explained! Dc.samizdat (talk) 10:19, 21 March 2024 (UTC)

@Dc.samizdat: I can take a look to see if I have any more specific suggestions, but I can say a few things right away. First, about half of Wikipedia readers aren't using a mouse, they are using a mobile device which cannot hover. Fortunately for me, I can click on explanatory notes and I get a popup overlay at the bottom on my phone screen. I'm not sure what other mobile browsers do. Second, people using text-to-speech screenreaders experience the article body first, followed by the footnotes at the end. If there are more than perhaps two or three explanatory footnotes, it is nearly impossible to remember the context in which they were encountered. Third, this is a relatively simple concept compared to say, the history of China, which requires huge amount of context to understand the whole thing, along dozens of disciplinary dimensions. The way we organize all that complexity is with linked articles that have names, which are easier to remember than more than an alphabet full of footnote letters. Each article is designed as a linear experience, starting with an overview that nearly everyone can understand, followed by progressively more difficult or obscure sections, so people who stop reading partway through (the majority) mostly get the parts that are most interesting or accessible to them. Fourth, Wikipedia content is often reused by search engines and may appear in print, in which contexts footnotes are often removed, so the linear text needs to work standalone. Fifth, an obvious target for reorganization is explanatory footnotes that themselves have explanatory footnotes. These are a terrible experience for screenreader users, and introduce cognitive load for visual readers trying to remember context, making the article considerably harder to read. If there are loops in the footnotes, it's possible to be unsure if you've actually finished reading the article or if you ever will. Sixth, we should expect about half of our readers are female. -- Beland (talk) 23:11, 21 March 2024 (UTC)

The first efn in the intro about the number of intersecting lines should be merged into the linear text in a detail section, though the phrase "curved 3-dimensional space" is confusing since it brings to mind relativistic effects and smooth curves. I think this is referring to a 3-dimensional surface which is folded into a 4-dimensional shape? Folding implies sharp edges and it's helpful to distinguish between shapes and the spaces they inhabit. The second efn in the intro about dimensional analogies seems off-topic and should be dropped or integrated into Four-dimensional space#Dimensional analogy. The caption "net" for the second image is not all that helpful; it should explain in a sentence or two how the four-dimensional shape was transformed into what is pictured. -- Beland (talk) 23:35, 21 March 2024 (UTC)

It's worth noting that when I click on a nested explanatory footnote, I can't navigate back to the parent footnote. -- Beland (talk) 04:08, 22 March 2024 (UTC)

Quite true, you can't follow your own idiosyncratic track back out of the rabbit hole, but you can see all the exit holes leading out of it to related concepts, and follow one of them, which is perhaps better for you, and a huge feature.Dc.samizdat (talk) 21:57, 22 March 2024 (UTC)

This is not a huge benefit; it's awful! I most likely wasn't done reading the parent footnote when I started reading the child one, and not being able to go back to the parent means I wouldn't be able to finish reading the explanation I was interested enough in to click on! Understanding this material is difficult enough when I can read entire paragraphs, but pulling partial paragraphs out from under me makes it not only more difficult to understand but frustrating enough I'm likely to stop reading about the subject just because of the poor organization. -- Beland (talk) 22:55, 22 March 2024 (UTC)

The efn definition of "completely orthogonal" has no citation. I do see a similar definition in Rotations in 4-dimensional Euclidean space, but it is in German and from the early 1900s. If this a commonly understood term, it should probably get its own article, which should just be linked from all the math articles that use it, including 24-cell. -- Beland (talk) 05:33, 22 March 2024 (UTC)

I fully agree that completely orthogonal should be its own Wikipedia topic. I believe it should be a section of Orthogonality (mathematics) rather than its own article, but I know that I am not the person qualified to write that section. Coxeter uses this term in 12 different contexts in Regular polytopes (book), but does not define it as such (it is so well-understood). For now I have cited Coxeter's first mention of it in my explanatory note, and also linked orthogonal in the note to Orthogonality (mathematics). Dc.samizdat (talk) 21:41, 22 March 2024 (UTC)

Thanks for the updated citation! The text has already been written in the form of the explanatory footnote. I have moved it to Orthogonality (mathematics)#Completely orthogonal, to which completely orthogonal now redirects. That efn had its own efn, which I merged into its parent and moved along with it. -- Beland (talk) 19:42, 24 March 2024 (UTC)

I have also merged the material from Rotations in 4-dimensional Euclidean space and dropped the duplicate material in 24-cell in favor of a link to completely orthogonal. -- Beland (talk) 19:53, 24 March 2024 (UTC)

Very good! I see what you mean about how I have committed the conceptual sin of putting one thing in two places. You're right that in cases like this I need to find the proper place for the undocumented concept, push it out to that place where it really belongs, and thereby get the proper distance between the concepts. You're right that it's much more confusing (as well as logically incorrect) to repeat definitions in multiple places. It is more work, however, I must not be lazy! This bad habit is quite distinct from my habit of writing lots of explanatory notes on how concepts relate to each other, however. A mere relationship is often too subtle to support a "home of its own" in a separate article, and that is why I have made such full use of explanatory footnotes as the only way to make the material comprehensible to the non-mathematical reader. Dc.samizdat (talk) 16:18, 29 March 2024 (UTC)

Were you planning to implement or respond to the other suggestions below? I could keep going through all the efns, but I stopped because I thought you'd probably be able to extrapolate what should be done for the rest. I'd rather leave the trimming in the hands of a math expert, but if it's more efficient, I could just start making changes. -- Beland (talk) 16:39, 29 March 2024 (UTC)

I am definitely going to respond to all your suggestions, and act on them, but you caught me at a particularly awkward time. I'm preparing something major for publication right now (in the real world, not for wikipedia) and I have a deadline coming up, so I haven't been able to give your talk page postings the attention they deserve. I have been reading them all, with great interest, and some frustration that I have not had time to respond to more than a few of them, but I just can't, it would be disastrous if I miss this deadline. Real world editors are slave drivers! :-) I promise to address your editorial comments properly as soon as I come up for air, but I will be slow about it for the next couple of weeks. Please don't feel obliged to actually fix all this stuff yourself, you shouldn't have to, and I would very much like to have the opportunity to do it myself. Dc.samizdat (talk) 03:24, 30 March 2024 (UTC)

No worries! In that case, I may add a few more comments while your attention is elsewhere, or maybe just go off and juggle all the other things I have in the air at the moment. 8) -- Beland (talk) 01:13, 6 April 2024 (UTC)

I should not have used the badly inverted colloquialism "real world", above, in referring to print media vs. Wikipedia. It is anachronistic usage, like my pronouns, but I fear I am getting to be an anachronism myself. Wikipedia is perhaps the most real medium we have, to the extent it is supported by references to reputable (real) publications in print media, where so much that is not real is also published. I do understand this. Dc.samizdat (talk) 16:33, 3 April 2024 (UTC)

There's an efn that starts off with the definition of a quarternion (currently "e"); that first sentence is very helpful. The part about Hamilton and the history of the discovery of quaternions is far off-topic and should be merged with History of quaternions if not redundant. -- Beland (talk) 23:55, 21 March 2024 (UTC)

I've cut the historical background about Hamilton, everything except the first sentence, leaving the link to Euclidean Geometry#Higher dimensions which contains it. Dc.samizdat (talk) 06:36, 16 May 2024 (UTC)

The "can be ordered by size" efn (currently "c") is probably best integrated into Regular 4-polytope#Regular convex 4-polytopes. The efn in this article gives a helpful definition of "size" which the ranking table in that article could use. I just added a clarification to the main body text which is all that's needed. -- Beland (talk) 00:36, 22 March 2024 (UTC)

Good idea! I have integrated this important explanatory note into the article to which it most naturally belongs, which is Template:Regular convex 4-polytopes, which is transcluded into the Euclidean geometry, 4-polytope and Regular 4-polytope articles and each of the 6 regular convex 4-polytope articles. I have removed, of course, the duplicate explanatory note in each of these articles, and added a Notelist template to the only one of these articles which did not already have one, so the annotated template expands without CITE error in every place where it is transcluded. Dc.samizdat (talk) 21:01, 5 April 2024 (UTC)

David Eppstein's removal of this efn from the template has left a dangling efn reference in Regular 4-polytope#Regular convex 4-polytopes. I agree with David's comments that if we're adding content it should go in that article, not the template. I also agree it should cite reliable sources (preferably with inline footnotes) or be dropped entirely, per the core policy of Wikipedia:Verifiability. -- Beland (talk) 01:10, 6 April 2024 (UTC)

OK, I will take care of that, including adding very specific authoritative citations for this content in Regular 4-polytope. And clean up the @Mikeblas edits that rescued my duplicate footnotes after @DavidEppstein's rollback left them dangling. I'll replace them with links to Regular 4-polytope#Regular convex 4-polytopes. Personally I think having the note in the template is better and should be allowed, for the reasons I expressed carefully, but that's just my opinion, and I understand it's a minority opinion that hasn't prevailed. I don't need it to. Thank you @Beland. Dc.samizdat (talk) 06:30, 6 April 2024 (UTC)

The efn that says "the edge length will always be different" (currently "d") seems a bit off-topic and unreferenced, and should probably just be dropped. -- Beland (talk) 01:08, 22 March 2024 (UTC)

I respectfully disagree. It describes a property that is unique to the 24-cell, of all objects in Euclidean spaces of any number of dimensions, and therefore precisely on-topic in the 24-cell article. It is from Coxeter, see reference [4] already cited in the lede of that article. I said "it seems" because although Coxeter says it, I have not found where anyone has given a proof of it. But you are correct of course that in the 600-cell article it is a duplicate footnote, where I shall remove it.Dc.samizdat (talk) 21:17, 5 April 2024 (UTC)

The efns in the section "Hopf spherical coordinates" should probably either be flattened into the main text or trimmed as excessive detail. I'm not sure how useful these facts are. It would help to cite sources showing these are not original research or excessively obscure; any uncited material would have to be removed anyway. -- Beland (talk) 05:38, 22 March 2024 (UTC)

Zamboj citation (Hopf coordinates of the 4-polytopes)

Denney citation (decagons and pentagons in the H4 polytopes) Dc.samizdat (talk) 06:24, 16 May 2024 (UTC)

Images in image captions are broken on the mobile version of Wikipedia, and have been for a while. Any images being kept need to be integrated into the main text. (There's one in what is currently efn "f".) Images seem like a fairly substantial piece of content; it seems odd to have them in footnotes anyway. -- Beland (talk) 05:43, 22 March 2024 (UTC)

BTW, the markup on this article does not comply with MOS:RADICAL; that page has instructions for fixing the broken-looking radical symbols. -- Beland (talk) 05:48, 22 March 2024 (UTC)

In the "Related" section, for brevity in an already long article for this density, can we just link to H4 polytope and drop the first table? -- Beland (talk) 05:59, 22 March 2024 (UTC)

For overall accessibility and maximizing what people get before they stop reading, it would probably be better to put the "Visualization" section before anything with math notation, if not the first thing after a generally accessible intro. -- Beland (talk) 06:56, 22 March 2024 (UTC)

The efn that starts "Consider the statement: In one full revolution" (currently "dp"[!]) sounds rather off-topic and also a bit like an original short essay - not prose that merely summarizes reliable sources. I was going to just drop it, but with better sourcing perhaps it would be helpful to merge something into Rotations in 4-dimensional Euclidean space. -- Beland (talk) 06:59, 22 March 2024 (UTC)

I've removed this Efn entirely. Dc.samizdat (talk) 06:20, 16 May 2024 (UTC)

Original research in efn

Please do not add original research or novel syntheses of published material to articles. Please cite a reliable source for all of your contributions. Thank you.

I have reverted your unsourced explanatory footnote in Template:Regular convex 4-polytopes. It appears to be original research and does not need to be spammed across all articles that use this template, nor any of them. —David Eppstein (talk) 21:10, 5 April 2024 (UTC)

deleting footnotes

Hey there! Looks like you've edited six or so articles this afternoon, each time removing an explanatory footnote and leaving behind a reference to an undefined footnote definition. This removed active material from each article, and also left it with an error about the undefined footnote name. I've fixed these up by reverting your changes, but I can't understand what it was you were trying to do. Do you need some help? -- Mikeblas (talk) 22:12, 5 April 2024 (UTC)

Thanks @Mikeblas for rescuing my dangling duplicate footnotes, which were left dangling due another editor's rollback of the single footnote-in-a-template I replaced them with -- you can read all about it above (see "Good idea!") if you want to, but this specific editorial decision has now been resolved, but I am still in the process of clearing away those duplicate footnotes and CITE errors once and for all; so no, I don't need help, but thank you! Dc.samizdat (talk) 07:08, 6 April 2024 (UTC)

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