Talk:Compound of five cubes

Alternate compound

Is the alternate non-isogonal compound of five cubes presented notable in any way? I can't find any reference to the object online. – OfficialURL (talk) 16:45, 23 March 2020 (UTC)

I doubt it. I removed the section and added File:Frodelius 5-Cube.png in Compound of four cubes. Watchduck (quack) 22:51, 20 June 2020 (UTC)

I removed it again, after ...A2E9/...6546 has reintroduced it. If this is not original reaearch (which I doubt), it could find its place in an overview called Compounds of cubes. (compare c:Category:Compounds of cubes) --Watchduck (quack) 21:52, 1 October 2021 (UTC)

The octahedrally symmetric 5-cube compound is a notable illustration of the regular 5-cube compound's symmetric transformations, and an example that, in particular, highlights the way in which the regular 5-cube compound's symmetry group is related to octahedral symmetry, through pyritohedral symmetry, via any of its component cubes. This is a non-arbitrary feature of the regular 5-cube compound's geometry. If the article is intended to be about only the regular compound of five cubes, then the octahedrally symmetric compound remains directly related to the regular compound of 5 cubes in particular. It certainly has significantly less relation to a compound of 3 tetrahedra. The article also is here to inform people of what a "compound of five cubes" is; not solely what the "regular compound of five cubes" is; hence the article's name, and also why, for example, the "dodecahedron" article is similarly not about only the "regular dodecahedron", which is itself a separate article. This is also in-keeping with a number of other articles on compound solids, and with articles on geometric solids in general, where, even when focused on a specific example, their extended geometric properties and geometric relations to other solids and symmetries are still noted in the articles. The purpose of the article is to provide a reader with information they might be looking for by searching for "compound of five cubes", which certainly includes pointing to more examples than only the regular compound of 5 cubes. There also isn't a prescriptive reason for this article being about solely the regular compound of 5 cubes. That is an arbitrary opinion that the article isn't obliged to reflect. And arbitrarily implementing that limit does not serve to improve the quality or contents of this article. And again, even fully taking that to be the case, the octahedrally symmetric compound illustrates an aspect of the regular 5-cube compound's symmetry group.

(If somebody is able to render a 3D animation of this, that would likely better reflect this feature of the regular 5-cube compound's geometry than the static image does.)

The octahedrally symmetric 5-cube compound was previously added to the compound of 4-cubes article, where it makes sense only as an example of a possible modification. In exactly the same way (as an example of modification), the same compound also fits in this article. And that is in addition to the rest of its reason for inclusion. The modification to the 4-cube compound is also non-continuous addition, while the symmetric transformation between the two 5-cube compounds is a continuous, symmetric transformation. That, plus the fact it is a 5-cube compound makes it fit more strongly in the "compound of 5 cubes" article.

If this article needs to be renamed to "regular compound of 5 cubes", then fair enough, but the vandalistic removal of relevant information isn't beneficial to this article, and renaming it in that way, to limits its focus, doesn't match the style of contents of a number of other similar and related articles. And it would also mean another article (analogous to "dodecahedron" versus "regular dodecahedron") would need to be made, which would be superfluous, given their overlap and needless differentiation. One article is more useful. An article listing symmetric compounds of 5 cubes also isn't really necessary.

Of additional note:

The octahedrally symmetric compound of 5 cubes isn't trivial or without precedent in academic awareness; what it lacks is literature, like many similarly specific solids. Of minimal note (of personal recent recollection), is its presence in a video (although it was not the topic or focus of the video), that was published by mathematician Grant Sanderson, visible here. This is being pointed to to illustrate that it isn't a flippant or trivial discovery being added for no reason. Still, whatever the focus of the article, this is relevant information to the regular compound's geometric properties. This clearly isn't an arbitrary addition. — Preceding unsigned comment added by 74.106.20.33 (talk) 11:20, 30 December 2021 (UTC)

I doubt that the "Frodelius 5-cube" is notable enough to justify a detailed description. That 3Blue1Brown used an image of it to illustrate the term symmetry is better than nothing. But I have seen no trace of a non-OR explanation, why this should by anymore than a side-note in Compound of four cubes. That "the symmetric transformation between the two 5-cube compounds is a continuous, symmetric transformation" sounds interesting, but is probably OR. (To be fair, this was mentioned only on the talk page, not in the disputed section of the article.)

This article is about the one notable compound of five cubes. Originally the first sentence reflected that:

The compound of five cubes is one of the five regular polyhedral compounds. This compound was first described by Edmund Hess in 1876.

I just realized, that it was also you who changed that to be more general:

A compound of five cubes is is a face-transitive polyhedron compound that is a symmetric arrangement of five cubes. This typically refers to the regular compound of five cubes.

I will also change that back to the original sentence. It seems, that no one except you believes this other compound should be here. Unless that changes, I will keep reverting your attempts to advertise the "Frodelius 5-cube". --Watchduck (quack) 12:32, 30 December 2021 (UTC)

This'll be a bit of a lengthy reply, I'm going to try to explain this a bit better. I'll add a TL;DR at the end.

long answer

I'm sorry if I've offended you. I get an impression - please feel free to correct me if I'm wrong on this - that you're taking this at least somewhat personally, and I'm not entirely sure why. I'm here for the mathematics and the education. I'm not trying to pick fights; I'm trying to better this article. But I don't follow your reasoning that "no one except me" believes the compound should be included. We're two people. Three, if you interpret the person asking whether the compound is notable as a claim that it isn't. But neither of us should try to take a position as if everybody else is on our side. I think most people don't care about this. And this isn't really about me; you don't need to try to make this an interpersonal feud. I don't have anything to do with the compound; personally, I'm a recreational mathematician who took a look at this article and noticed that there was some information relevant to the topic that was, for some reason, was missing. The geometry is a fact about it with or without me or somebody else putting it back in a Wikipedia article; all I wanted was for the article to have more and better information on the topic that it is about. I doubt that the "Frodelius 5-cube" is notable enough to justify a detailed description. That is a fair opinion to have. But it is opinion. My opinion is the opposite, because the octahedrally symmetric 5-cube compound has a direct link to the regular 5-cube compound through their groups. The opinion that it isn't notable is, to me, not a strongly substantive reasoning to delete that information. And it is sort of tautological, the fact it isn't a solid often noted being a reason to subsequently not note it. This is already a very niche article to begin with. The information on the octahedrally-symmetric 5-cube compound was being noted as a feature of the regular 5-cube compound's geometry and symmetry group. Which is information about the topic of the article, irrespective of the article's scope being a family of solids or of a specific example. There are many other symmetric 5-cube compounds. No others in that family (to my knowledge) share this specific symmetric relationship. But I have seen no trace of a non-OR explanation, why this should by anymore than a side-note in Compound of four cubes. Well, for a start, if a compound of 5 cubes warrants inclusion in the compound of 4 cubes article, based on the reasoning that it can generated from the latter, it then still also belongs on this article as - at the least - a similar side-note, for exactly that same reason. The difference being that it is generated from either in different ways. Also, I want to point out, this isn't original research. Actually, I'm not sure if it could be considered original research, because the geometry is an irremovable part of the solid, no matter what person might be writing it on Wikipedia. But this geometric relationship is also visible from the image (insofar as a person can visualize the transformation from seeing the relevant coincident vertices). But the explanation for its inclusion is largely that anybody looking up "compound of 5 cubes" would likely find it - at minimum - passingly relevant to the nature of the regular 5-cube compound. I certainly find it relevant in a few ways. Hence adding it. The rationalization that only a small number of people has so far thought to include it, isn't a reason against adding it. To be fair, this was mentioned only on the talk page, not in the disputed section of the article. I feel like I should point out that the information is in that section. It was outlined more formally (maybe a shorter description with less information would satisfy what you consider an appropriate level of informativeness), but it is the same information about the same geometric transformation. The point of inclusion is that the symmetry group that the regular 5-cube compound has, and its arrangement of cubes, allows it to undergo a continuous, symmetric transformation (via rotation of its cubes around the diagonal axes of its coincident vertices of a reference cube) through a phase of pyritohedral symmetry, to octahedral symmetry (the compound being challenged), which is a transformation analogous to the transition between a regular dodecahedron to a rhombic dodecahedron, but one which doesn't involve deformation (taking the cubes to be individual bodies). I will also change that back to the original sentence. That being your position, there are a number of other similar articles that you probably will want to edit to make them match this one. The reason for that change was given as "the article previously used wording that may have mislead readers by implying the existence of only one symmetric 5-cube compound". That issue still absolutely still remains a valid reason to preserve the improved explanation of the compound overall first, before explaining the regular compound specifically, for the sake of a reader's accurate understanding of the topic. Phrasing matters. Misleading readers - even accidentally - would be a bad call to make. Making it clear that this article is about one example, rather than the only example, is better phrasing. Also, I'm going to stop addressing whether the scope of the article should be about what the regular 5-cube compound is, or the topic of what a 5-cube compound is. Articles contract and expand scope all the time. That debate really doesn't have an impact. In both cases, excluding mention of solids related directly to the regular 5-cube compound is not beneficial. It is - I would strongly argue - information that fits there. It is - in some meaningful sense - a part of the regular 5-cube compound. "attempts to advertise" Personally, I'd appreciate it if you'd pull in the reigns on that kind of rhetorically charged language and opinion. I'm really trying to keep redirecting this back to the topic of the article. The kind of phrasing you're using tries to impose an opinion of why the information was re-added. It isn't advertisement. The mathematics of it is there without me, and I am trying to better the article, and trying to accomplish that with professional explanation. You're sort of trying to turn this into a personal feud, instead of helping to make the article an informative one. The "I will keep reverting your attempts" stance send a message that you've completely already made up your mind to keep the article's informativeness narrowed, and also making that personal. You've used wording like "not an overview of any conceivable compounds", which seems to deliberately overexaggerate the scope of the information being added, and the intention behind it (this is 1 compound related to the regular compound directly, and the explanation of how being included; not all symmetric 5-cube compounds being added for the sake of having a list), and "Just write Compounds of five cubes, if you think this matters.", which - at the very least - reads like a dismissive tone; it is important to this article, and "Your contraption" (I don't own the octahedrally-symmetric 5-cube compound, and calling it a "contraption" reads as deliberately derisive), and the "Look, I have discovered another compound!" thing in your editing, and the "no one except you believes this" assertion. Plus the emphasized "*the* compound of five cubes" in your last edit, even though you're aware that it is the regular compound of 5 cubes, specifically. It isn't constructive to treat Wikipedia like something to win and then try to flaunt. And a feeling of self-rightness isn't constructive. This compound doesn't have much literature. I am aware of that. That is one reason to improve this article. It isn't a flippant whim of discovery somebody is looking to flaunt for no reason on a whim. The mathematics is there. Personally, I find it relevant, which is why I wanted to re-add it. Trying to arguing I'm the "only" person who thinks it should be added isn't really an argument. Somebody is present, visibly saying it should be added. The case is being made. Dismissing it because the case isn't being made enough isn't listening to the merits of the case itself. The best I can do, given its lack of literature is point to the only recent example I can both recall and locate, which was Grant Sanderson's video. I'm aware it isn't ideal. The point is that "Look, I have discovered another compound!" isn't what is happening here, and other mathematicians are aware of it. It isn't an advertised contraption. It is difficult to find what writing on it there is, in particular because the regular compound is much more widely discussed. The octahedrally symmetric compound of 5 cubes is a niche detail of the regular compound, and it also is a compound that can be taken in isolation. It can be thought of or framed either way. And it is being framed as relating to the regular 5-cube compound here. That is the point. Please stop trying to make this about me. You don't know me. I'm interested in improving an article; not a fight. I don't know you either.

TL;DR: The octahedrally-symmetric 5-cue compound isn't an arbitrary re-addition to the article of an unrelated compound being presented as a new discovery. The symmetry group of the regular 5-cube compound links it - through a continuous, non-deforming transformation of its component cubes rotation about the axes of their and the reference cube's coincident vertices - to octahedral symmetry (in the compound being challenged), through pyritohedral-symmetry. That is a feature of the compound's geometry. Aspects of it are listen in other parts of the article in other ways, but this relationship not stated. If the way the information is presented is a problem, absolutely, I'd encourage presenting it better. Probably you know those standards better than me, but I do very strongly believe the information that was added and then removed is information now missing from this article that belongs there, on the topic of the article. And if the only thing you want is literature, that does seem bizarrely stringent for an extra bit of information on this compound, and if that really is where you draw the line, then the article lacks information unless some mathematicians out there want to write formal literature on it. Either way, it definitely makes more sense included as a side-note here than in the 4-cube compound article. — Preceding unsigned comment added by 74.106.20.33 (talk) 16:14, 30 December 2021 (UTC)

This answer is indeed absurdly long.

Concerning "advertise", "contraption" etc.: Your changes to this article could be interpreted more benevolently than I did. If you were a user with a general interest in improving geometry articles, I would be more inclined to do that. But I can't help but notice that all your edits aim at adding this compound to this article. That makes you seem more like the kind of user who wants to push their pet issue into other peoples faces.

Anyway, somewhere in that oversized answer you could have mentioned, that the rotation angle is 2*arctan((sqrt(5)-2)/sqrt(3)). That was a bit of a pain to calculate.

I have made some illustrations of that transition, which can be found on Commons. I will add other images, including animations.

This is indeed quite cute, and I would not mind adding an animated picture of the transition to this article.

I just realized, that the Wolfram article Cube 5-Compound shows a tiny picture of your compound, and calls it "first cube 4-compound".

The cube 5-compound can be inscribed on the vertices of an augmented dodecahedron, (first) cube 4-compound [...] Deltoidal Hexecontahedron [...]

I think that justifies a short section in Compound of four cubes. I would not add a "can be inscribed" list to this article. --Watchduck (quack) 02:55, 31 December 2021 (UTC)

all your edits

From this IP address. Maybe this point might need a clarifying, because of the impression there seems to be of the editing. I use a VPN, and have to change my settings to be able to contribute to Wikipedia articles. All the edits from this current IP would be only the edits I've done today, yes. I try to improve articles on mathematical topics every so often, when I notice room for it. My IP address isn't permanent, because of the security settings I use, and, because I don't make edits extremely often, all those other edits wouldn't end up being attributed to this current IP address (which is on top of other internet stuff; not important). Don't worry, I respect all the normal rules, including blocks. The quick point is that this editing wasn't some random one-off overzealousness, which seems to have been the impression. I completely get why it would appear to be that.

"That makes you seem more like the kind of user who..."

To you, which - if that is still the impression you have, given the VPN clarification - I'm alright with being the case as well as the opinion of my reply being "absurdly long" and an "oversized answer". I am still trying to steer away from that kind of an interpersonal stuff, though. I was mostly trying to avoid miscommunication as best as possible. There seemed to be a lot, on my side too, regarding the purpose of what the information was describing, in relation to the scope of the article's topic. It seemed the correct place for the information in question. I think an understanding is being reached now, in that the symmetry transformations could be presented more concisely, and it made more clear how this symmetry transformation is directly related to the symmetry group of the regular 5-cube compound, rather than it being presented in a way that could give it the impression of being a standalone, other compound mentioned aside for no particular reason. The animations would obviously be sufficient in conveying it. Rendering those images and animations is without my wheelhouse, so I considered the prewritten, text-based description of the nature of that geometry serviceable. Definitely the animations would convey that property of this geometry in way less space. I very much appreciate the rendering of the transition in the Wikipedia commons. The fact this transitional symmetry relationship now has extant visual demonstrations is a significant contribution to insight on the topic, and that is the core of why I considered the text version worth re-addeding. It is appreciated. A simple animation showing the transitional relationship of the symmetry groups does seem an ideal solution to what should fit in this article. — Preceding unsigned comment added by 74.106.20.33 (talk) 05:32, 31 December 2021 (UTC)

I have added a section in Compound of four cubes, and a picture of the animation in the See also section of this article.

Would you mind if I put the non-TL;DR part of your long answer in a collapsible box (like I did here)? --Watchduck (quack) 13:23, 1 January 2022 (UTC)

I would not mind. By all means. — Preceding unsigned comment added by 74.106.20.33 (talk) 21:31, 1 January 2022 (UTC)