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The cube can be represented in many ways, one of which is the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs.
The cubical graph is the edge graph of any quadrilateral hexahedron, regardless of any symmetries, so can it be said to represent the cube rather than the more general shape? —Tamfang (talk) 19:04, 7 March 2025 (UTC)[reply]
@Tamfang I am hoping this could be written for cuboids and any quadrilateral hexahedron. But for some reason, I cannot find the source. Also, I prefer to expand the graph section for more. Dedhert.Jr (talk) 02:33, 8 March 2025 (UTC)[reply]
I noticed that this article was nominated for GA and I skimmed through it and noticed that there's a paragraph about cubes in popular culture (the first paragraph of "Applications"). I was wondering if it would be beneficial to split this paragraph off to its own section (or subsection) for cubes in popular culture and add a second paragraph in that section for cubes in fiction or just add that paragraph to the existing Applications section. Some widely known fictional cubes: the cubes in the Cube movie franchise, Borg ships in Star Trek, the Weighted Companion Cube in the Portal games, and Bizarro World in the DC comics. These four all have their own Wikipedia articles that could be linked to. Velayinosu (talk) 00:52, 18 June 2025 (UTC)[reply]
The application is intended to explain the usage of a cube in the real world; architecture, arts, and science commonly use the cube. However, speaking of popular cultures in the case of fictional films and movies, maybe WP:POPULARCULTURE. Unless there are mathematical sources attributed to these fictional cubes, one can take a sample from Mobius strip#In popular culture. Dedhert.Jr (talk) 02:07, 18 June 2025 (UTC)[reply]
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
I've wanted to review a maths article for a while, and this seems (mostly) simple enough for even I to get my head around. Comments to follow within a couple of days.
I am very glad to take a review of this article. Mostly, I was focusing on the structure, including the writing, although @Tamfang helped with the grammar correction (thank you btw). I'll give my best. Dedhert.Jr (talk) 11:48, 27 June 2025 (UTC)[reply]
A. It contains a list of all references (sources of information), presented in accordance with the layout style guideline:
B. 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):
Firstly, congratulations on making the article so readable even while being pretty complicated at times Dedhert.Jr; there are a couple of occasions where the grammar could be improved, so would you permit me to give the article a light copyedit? Otherwise, all good with the prose re. criterion 1a). ~~ AirshipJungleman29 (talk) 11:37, 28 June 2025 (UTC)[reply]
@AirshipJungleman29 No problem. It's actually helped me more than my own writing, and I hope I can take this to FA someday (please let me do it; I really want to learn it, so I might have to ask in PR, but for now, we might tend to focus on GACR). For the images, I have no idea how to add a US tag public domain, so can you tell me how? Dedhert.Jr (talk) 11:58, 28 June 2025 (UTC)[reply]
Excellent. Yes, I think helping to an FA standard might be too much for me—you'll have to ask other WT:MATHS participants, but please do ping me if you ever nominate it there. I have copyedited the article; let me know if there are any changes you disagree with (it's entirely possible I misunderstood something and rewrote it incorrectly). I'll do the US copyright tags; please pay attention for the future. I would also like clarification on the following sentence from you or Tamfang: "Its automorphism group is the order of 48" is this grammatically correct? ~~ AirshipJungleman29 (talk) 13:01, 28 June 2025 (UTC)[reply]
I am neither the nominator nor Tamfang, but I do find that sentence to not be grammatically correct, I think writing it as "Its automorphism group has order of 48" would be more grammatically correct, but I think also calling them Isometries, as in "There are a total of 48 isometries for the cube" would be a bit more clear to the reader if they are less familiar with the automorphism group, see Octahedral symmetry#The isometries of the cube. Maybe these two can be combined as in "There are a total of 48 isometries for the cube, which corresponds to the order of the cube's automorphism group." Gramix13 (talk) 16:06, 28 June 2025 (UTC)[reply]
I am not 100% sure if Cubism is applied from the cube. Although some of the arts used the shape of a cube, the representation of multiple perspectives differently shows the line and color thingy. I might not be skilled in historical art, so one can ask on a WikiProject. Dedhert.Jr (talk) 09:33, 29 June 2025 (UTC)[reply]
The one thing I think does need a bit of work is the lead section: per MOS:INTRO, it needs to be accessible to as broad an audience as possible, avoiding difficult terminology and jargon. Per WP:ONEDOWN, you can easily imagine that the article will be read by very young children who are just starting to learn about shapes. In this context, the lead needs to be simplified, especially the first paragraph, where even comparatively simple words such as "congruent" could be too high-level. ~~ AirshipJungleman29 (talk) 13:49, 1 July 2025 (UTC)[reply]
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.
Holy cube. What a dope opportunity for DYK to have to showcase this article. Was just recently improved to GA status, so it clears new enough criteria. That GA status also presumably allows for the article (and hook) to clear long (or for hook, short) enough, well-sourced, and presentable criteria. Can confirm after doing a quick double-checking of that on my end. QPQ does not apply here. ALT0 is good to go, but given the scope of the article and the plentiful amount of great images on it, I would definitely support any ALT hooks being developed here. As a result, this is a potential image+hook candidate for the DYK section too. For sure good job on this. Soulbust (talk) 12:44, 7 July 2025 (UTC)[reply]
@Soulbust. Perhaps there are more alternative hooks:
ALT1: "... that there are 11 ways to unfold a cube?"
ALT2: "... that cubes have a hexagonal cross-section, used as the floor in Dutch cube houses?"
ALT3: "... that cubes appear in the shapes of both crystals and microorganisms?"
Those are all very interesting (honestly like ALT1 or ALT3 about the unfolding or shape, respectively), but unless my ctrl+f missed it, they aren't mentioned in the article, which they would need to be for DYK purposes. All good either way. If they can't be added into the article for whatever reason, no worries, wouldn't want that to hold up the promoter from accepting this and running with ALT0, which is definitely interesting itself. Soulbust (talk) 12:58, 7 July 2025 (UTC)[reply]
I just finished reviewing this at Wikipedia:Peer review/Cube/archive1. I hope I'm not breaking any rules by also reviewing it here. I really want to promote ALT1, but the facts in the hook are scattered across two different parts of the article. Construction talks about "eleven nets", but doesn't talk about unfolding. If you could add something which explained that "nets" is about unfolding, we'll be good to go. RoySmith(talk)20:44, 22 July 2025 (UTC)[reply]
The eleven nets of a cube
Actually, even better would be:
ALT1a: "... that there are 11 ways (pictured) to unfold a cube?"
I won't mind changing the hook. My original hook is to target young generations who are interested in games nowadays. But I think this is obvious for most of them. Dedhert.Jr (talk) 03:13, 23 July 2025 (UTC)[reply]
@Soulbust: As the original reviewer, can you check ALT1a? If approved, please add another green DYK tick below and if not, please outline what else needs to be done. Thanks. Z1720 (talk) 16:51, 29 July 2025 (UTC)[reply]
@Z1720: Hi yeah, it looked like RoySmith's concerns/comments about the Construction section mentioning eleven nets, but not how those nets are related to unfolding, was still true --- unless I was missing something. I just went ahead and added that sort of explicit clarification into the article myself, with a new source. Should be good to go now. Soulbust (talk) 21:42, 31 July 2025 (UTC)[reply]
I am attending to a request to peer review, alongside nominating a DYK's hook for featuring on the main page, for improvement according to WP:FACR. Hopefully, this article will become a potential for FA. Any feedbacks would be appreciated.
This is a really nice presentation. So many math articles dive head-first into technical details that I'm lost before I get to the end of the first sentence. I'm up to Relation to the spheres right now, and still following every word, so that's great, and a great example of WP:MTAU. For context, I was an engineering major in school, so a decent math background, but not my main thing. And I got a head-start on polyhedra by playing lots of D&D in high school :-)
I'm up to Applications now and the reading is getting a little slower, but that's good. Easy at the start, diving deeper into technical esoterica as the article progresses. As it should be.
As a general comment, you do a pretty good job of explaining technical terms, but there's a few more which could use a short in-line definition: cubiod, dihedral, interior angle, Euler characteristic, orthogonal, parallelepiped, congruent, rhomoohedron, trigonal trapezohedron, centroid, isometries, dual (and in dual polyhedron), tesseract, crown graph, bipartite Kneser graph. I'm going to assume that anybody reading this will not have any problem with edges, vertices, faces, polyhedron, or platonic solid.
I had never heard of the Prince Rupert's cube, but I had heard of the Prince Rupert's Drop, which I see are named after the same person. Might be worth dropping that little bit of coolness into the article.
doubling the cube ... compass and straightedge ... Ancient mathematicians could not solve this problem until the French mathematician Pierre Wantzel proved it was impossible in 1837 But it is possible with origami, which is another bit of coolness you could drop in here. But more to the point, this is worded strangely. They still couldn't solve it after 1837, but at least then they knew why.
five cut the cube from the midpoints of its edges, and four are cut diagonally make the gramatical constructions, ahem, conguent: "five cut the cube from the midpoints of its edges, and four cut diagonally"
(image caption) A six-sided dice Ugh. "Dice" is plural. The singular is "die"
Not sure you need to mention this, but Alamo not only sits on a vertix, it spins around its vertical axis. That was my old stomping grounds, and I have indeed spun it. It takes a few people; the bearings aren't very good. But read WP:POPCULTURE and consider how much of this section you really need.
Pyrite is an example of a mineral with a commonly cubic shape Maybe use common table salt as a more familiar example?
That about does it for me. I don't think this will have any problem at WP:FAC but you should enlist somebody with a stronger math background than me to take a look at it. I'm thinking David Eppstein would be a good possibility. RoySmith(talk)20:28, 22 July 2025 (UTC)[reply]
@RoySmith. I think I have completed most of suggestions. You might want to read it by yourself about my writing that is somewhat a little bit of overdetailed. Dedhert.Jr (talk) 03:42, 23 July 2025 (UTC)[reply]
@Dedhert.Jr just wondering where things are with this. I'd really love to see this at FAC. We have so few high-quality math articles that are written in a style approachable to people who aren't hardcore match geeks, and this would make a great addition. RoySmith(talk)22:00, 17 September 2025 (UTC)[reply]
This article is about a mathematical object commonly known to the public as the cube. WikiProject Mathematics has fewer FA than GA, approximately one in seven, especially WikiProject Polyhedra, which has zero FA, excluding the three FA biographies. Since then, I will take this to FAC for the first time. Support, oppose, or any miscellaneous opinion is handed to the participating reviewer.
In the "Appearances" section, it is written that Salvador Dalí's painting Corpus Hypercubus (1954) contains a tesseract unfolding into a six-armed cross; a similar construction is central to Robert A. Heinlein's short story "And He Built a Crooked House" (1940).; however, the lede says that the tesseract is a member of the same family of polytopes as the cube, so I would not expect that this is an appearance of the cube. I would remove this sentence from "Appearances", or at least move some of its content to the mention of the Dalí cross in the "Polycubes" section.
I would rather move out to the polycube sections, while maintaining the fact that the cube is used to stack to form a Dali cross, which is used in popular cultures. Dedhert.Jr (talk) 04:04, 24 September 2025 (UTC)[reply]
A layman would perhaps expect that "Construction" is more explicit. Something about folding on the edges and gluing the sides might be helpful in the first sentence.
When all of its interior angle (the angle formed inside) are right angles, -- should this be "interior angles" and "angles"?
Angle can vary (dihedral, exterior, interior, etc.). An interior angle is an angle within a polygon; alternatively, you can say it is an "internal angle". No clue if the U.S., U.K., or any English-language countries worldwide actually use it. Dedhert.Jr (talk) 04:04, 24 September 2025 (UTC)[reply]
I meant rather to ask whether "interior angle" and "angle" should be plural rather than singular.
Prince Rupert of the Rhine, known for Prince Rupert's drop, questioned whether a cube could pass through a hole cut into the unit cube. Despite having sides approximately 6% longer, such a cube can pass through a copy of itself of the same size or smaller -- what "such cube"? Where does 6% come from? Perhaps this could use more explanation, especially since Prince Rupert's cube is used as an image but not explicitly mentioned, being hidden behind the wikilink in the quote.
Later note: I think that this sentence is simply poorly worded. The sentence Despite having sides... suggests that Prince Rupert's cube has already been introduced; I would instead write something like "In fact, a cube of side length 1.06 can pass through a unit cube". I find the phrase such a cube can pass through a copy of itself of the same size or smaller confusing as well: can't any cube pass through a copy of itself?
You do mention dice at the beginning of the section, which is why I suggest that location. I was wondering if the oldest known manufactured cubes were dice, which I would think is likely, though it seems equally likely that no reliable source discusses this.
I was pleased to see this show up here this morning, since I recently prodded Dedhert.Jr to do so. I left some comments at PR, but doing another pass now...
A cuboid is a polyhedron that consists of ... This is the lead-off sentence of Properties, so I would expect it to start with "A cube is ...". Then drill down into "It is a special case of ..."
every face of a cube has four vertices, each of which connects with three lines of the same length The standard geometric definition of a line is that it's infinitely long, so "three edges of the same length" would be better.
Every three square faces surrounding a vertex are orthogonal to each other "Every three" could be read as "Every third". How about "All of the three ..."?
Other special cases for a cube are ... Between the parentheticals set off by dashes and the list of things, this is quite a complicated sentence. How about, "A cube is also a special case of a parellelepiped, a rhombohedron, and a trigonal trapezohedron." followed by three sentences, each one describing one of those and why a cube is one.
Alternative option, "A cube is also a special case of other cuboids. These include...". At least I have tried to maintain while replacing dashes with commas. Better? Dedhert.Jr (talk) 04:04, 24 September 2025 (UTC)[reply]
I've come back to read this section again, and I'm afraid it still doesn't make sense. The text Prince Rupert ... questioned whether a cube could pass through a hole cut into the unit cube is incomprehensible. I *think* what you mean is "asked what is the largest cube which can pass through ..." but I'm not sure. I have no idea what to make of The answer is that the cube can pass through a copy of itself of the same size or smaller. The diagram doesn't help any. If a better diagram can't be found or constructed, I'd leave it out. There's an excellent animation at https://www.youtube.com/watch?v=ua4LadxA6K8; perhaps you could write to them to see if they would be willing to uplodad it to commons? I also found File:Rupert-Cube.webm, which isn't wonderful, but is at least better than the current image.
There's also a few different things smashed together into one big paragraph that wanders from one subject to another. I'd break out Rupert's cube and doubling the cube into their own paragraphs. RoySmith(talk)14:43, 4 October 2025 (UTC)[reply]
See Prince Rupert's cube: Prince Rupert's cube is named after Prince Rupert of the Rhine, who asked whether a cube could be passed through a hole made in another cube of the same size without splitting the cube into two pieces.
Instead of smashed together into a big chunk paragraph, I would rather split into a new subsection, and also follow yout suggestion. Dedhert.Jr (talk) 01:07, 5 October 2025 (UTC)[reply]
OK, but the point is, in this article, we've got something that makes no sense standing on its own: ... questioned whether a cube could pass through a hole cut into the unit cube. The answer is that the cube can pass through a copy of itself of the same size or smaller. Its edges are 6% longer than the unit cube, obtained by the Pythagorean theorem or equivalently the formula for Euclidean distance in three-dimensional space is basically incomprehensible, so that needs to get fixed. RoySmith(talk)02:13, 5 October 2025 (UTC)[reply]
Well, that's better, but what does "the 1693 English mathematician John Wallis" mean? I also don't see anything in the cited source that talks about errors in Wallis's proof. RoySmith(talk)14:44, 6 October 2025 (UTC)[reply]
As I mentioned in the PR, while you can't double the cube with a compass and straightedge, you can do it with origami and I think that's worth mentioning here.
My only comment here is that the last bit, where you talk about the platonic solids, seems to go off on a bit of a tangent with Kepler's model of the solar system. That could probably be trimmed a bit.
In the In orthogonal projection section, I'd start by making a statement about the cube, then going on to explain what it means: "The cube is equiprojective. That means ..." This also seems like it would benefit from a diagram.
The cube is a non-composite polyhedron, meaning there is no plane intersecting its surface only along edges, by which it could be cut into two or more polyhedra this doesn't seem to belong in this section. It seems more like a statement that should go in Properties.
OK, that's it from me. Overall, I think this is wonderful. Most math articles dive into advanced concepts in the first paragraph (if not the first sentence) making them impenetrable to anybody but an expert. This article starts out nice and easy and slowly adds complexity as it goes along. My guess is anybody who took high school geometry should be fine for at least the first few sections (say, up to about Symmetry), so that's pretty good.
OK, now that we've got Rupert sorted, I am happy to support. I'll leave you with one thought, however. What makes this article really appealing to me is how approachable it is to non-expert readers. As this FAC continues, I expect there will be pressure to add more stuff. Try to resist that, and if you can't, then at least keep looking for ways to keep the presentation at a level that would appeal more to a high-school geometry student than to a post-graduate math major. And if you are forced to add advanced material, add it near the end, so the reader can slowly ease into the more difficult material without getting blow away in the first sections of the article. RoySmith(talk)13:45, 8 October 2025 (UTC)[reply]
Overall, looks like a spectacular article! And it's a level-4 vital article. Illustrations are colorful & informative. Agree with User:RoySmith that it is inviting even to laypeople.
Lead: The cube was discovered in antiquity... "discovered" doesnt sound right. One discovers a planet or island. Consider "identified" or "described" or "documented" or "recorded" etc
Fair enough. What does the source used by this article as the basis for the statement "The cube was discovered in antiquity... " say, verbatim?
Lead: It can be derived differently to create more polyhedra, and it has applicaftions to construct a new polyhedron by attaching others. I gather that this sentence is trying to summarize the body sections "Truncation" and "Other polyhedra's construction", correct? The second part of the sentence kinda makes senswe; but I have no idea at all what "It can be derived differently to create more polyhedra " means. I think the entire sentence needs to be rewritten to be clearer.
Clarify: Some of its types can be derived differently in the following: ... The word "type" here appears to be a term of art. What does it mean in this context? I looked above in the article and could not find a definition. Perhaps link "type" to a WP article that defines what it means.
Clarify: Some of its types can be derived differently in the following: ... The word "derive" here in a math article is confusing me. One can derive a formula; or take the derivative of a function. But the text following this appears to be describing ways new polyhedra can be constructed by altering a cube. I made cardboard models of all the Platonic & Archimedean solids when I was much younger, so I'm familiar with the process. Wouldn't it be more accurate to say Some of its types can be constructed ... Or, if "derived" is a term of art, link to the WP article that defines it.
Clarify: Some of its types can be derived differently in the following: ... What is the purpose of the word "differently"? Suggest reword the sentence e.g. Many polyedra can be constructed based (or "from") on a cube. Examples include: ...
Spell-out more clearly: Both cube and tesseract are known as three-dimensional and four-dimensional hypercubes, respectively. I think readers would benefit from a more basic statement such as A cube is a the 3-dimensinal instance of an n-cube (also called a hypercube). The 2-dimentional n-cube is a square; and the 4-dimensional n-cube is a tesseract.
Plurals improved?? which can be modeled by the arc of great circles, ... That singular "arc" does not sound right to my ears. Maybe ...modeled with great circle arcs... or ... modeled with the arcs of great circles...
Cite uniformity: Need to have ISBN for all books. E.g. Richeson, D. S. (2008). Euler's Gem: The polyhedron formula and the birth of topology. does not have ISBN
Cite uniformity: All or no books should have "location" field. Most do not, but some do e..g Thomson, James (1845). An Elementary Treatise on Algebra: Theoretical and Practical. London: Longman
Cite uniformity: Many journals do not have WP articles; inconsistency in cites: most of them are black text but one is red text: Milan Journal of Mathematics. All should be black.
A cite validation tool is reporting an error "DOI invalid" on this cite: Rudolph, Michael (2022). The Mathematics of Finite Networks: An Introduction to Operator Graph Theory. Cambridge University Press. p. 25. doi:10.1007/9781316466919
Ambiguity: . One of them, the cube, represented the classical element of earth because of its stability. What was stable? the cube? the element? or the earth?
Cubes are also found in natural science and technology... [Science here]... Other technological cubes include the... .[Technology here] Consider changing "Other technological cubes" to "Technological cubes" since the tech is after this, not before.
... leading to the use of the term cubic to mean raising any number to the third power... I know WP is not a dictionary, but perhaps the article could more directly state something like As a verb, cube means to raise a number to the third power in addition to (or instead of?) this green text?
Source titles: capitalization uniformity: Titles of all sources should all use same cap rule. The article has a mixture e.g. "The Mathematics of Finite Networks: An Introduction to Operator Graph Theory" and "Fullerenes and coordination polyhedra versus half-cube embeddings" WP does not require the article to follow the capitalization used by the orig author of the source. Uniformity is preferred.
Clarity & general/special sequence: The cube has a Dehn invariant of zero, meaning that cubes can achieve a honeycomb. It is also a space-filling tile in three-dimensional space in which the construction begins by attaching a polyhedron onto its faces without leaving a gap. Can you improve this to clarify the distinction (if any) between (a) honeycomb; (b) space-filling tile; and (c) 3D tessellation of space? If those descriptors are all synonymous, say so. If not synonymous (and the cube is all three of them) then add a few words distinguishing.
Is the cube special regarding filling space? One of how many? The cube has a Dehn invariant of zero, meaning that cubes can achieve a honeycomb. It is also a space-filling tile in three-dimensional space in which the construction begins by attaching a polyhedron onto its faces without leaving a gap. I understand there are an infinite # of arbitrary polyhedrons that can fill space; but what about plesiohedron/regular/other polyhedrons? How many of them can fill space? Then tell the reader: The cube is one of 500 plesiohedron/regular/other polygons that can fill space. Here, where I have "plesiohedron/regular/other" I'm suggesting the article select one of these that only has a finite # that fill spacae and is interesting.
Color key? Image File:The 11 cubic nets.svg has 3 colors. Either (a) if the colors are significant, then explain the significance and change image to follow MOS:COLOR for color-blind readers; or (b) if colors not significant, then explain that in the caption, or use same color for all. That is an SVG image, so it is easy to change the colors - if you need help, let me know.
I think the current one is the best, it's just a matter of understanding what the colors mean. I did a little poking around and discovered this is a subset of the 35 free Hexominos and the colors represent the symmetry groups, which might be useful to add here (appropriately sourced, of course). Pinging Nonenmac who drew the original image and might have additional insights. RoySmith(talk)11:22, 25 September 2025 (UTC)[reply]
@Dedhert.Jr - I don't have a specific preference on blue vs others. To clarify the concerns:
If the images use multiple colors, the colors should be explained
If the images uses multiple colors, the image must comply with MOS:COLOR accessibility color-blindness guideline.
Replacing the colors with patterns (hash lines, dots, solid etc); or
Using varying LIGHTNESS (e.g. white, pink, red) rather than HUE (e.g. red, grey, blue).
MOS:COLOR implies that the image caption should describe the individual color meanings with Template:legend e.g. {{legend|#FF3333|Symmetry class A.}} Caption should not say things like Red means symmetry class A.
Sigh. Regarding Special:Diff/1313280598, this certainly fixes things in the sense that it no longer violates WP:COLOR, but you've fixed it in the wrong direction. You went from "People with color-impaired vision can't see the symmetry information" to "Nobody can see the symmetry information". RoySmith(talk)15:56, 25 September 2025 (UTC)[reply]
My apologies for harping on this, but that's just another example of You went from "People with color-impaired vision can't see the symmetry information" to "Nobody can see the symmetry information". The original image just needed some tweaking to pick three colors would be distinct even in greyscale and add an appropriate legend. RoySmith(talk)19:26, 25 September 2025 (UTC)[reply]
Symmetry group X
Symmetry group Y
Symmetry group Z
Yes, that was my intention, since Jens Lallensack said that they preferred the original image. But I've made a monochrome image with a legend as well, which I've included here. Pagliaccious (talk)19:48, 25 September 2025 (UTC)[reply]
Agree with RoySmith. To change the colors in the original image, simply edit the colors in the SVG file:
.t { fill : #AAA } .u { fill : #D99 } .w { fill : #AAD }
For instance, a change to:
.t { fill : #2222BB } .u { fill : #7777FF } .w { fill : #CCCCFF }
Section title? Section "Appearances" has an unusual title. Is that a Math Project thing? I'm accustomed to seeing "In culture" or "In nature" etc. Consider breaking that section into 2 or 3 sections: one for nature/science; one for humans/arts/literature/history.
Appearance is basically where an object appears in real life, in whatever era. Some polyhedral articles are named the section "Applications", indicating an object is used as a tool in real life, but it is incompatible with the discovery of biological shapes. Breaking into two or three subsections seems not a bad idea, as long as there are more sources mentioned about those three individually. This might answer the next comment. Dedhert.Jr (talk) 10:56, 25 September 2025 (UTC)[reply]
CGH cube sentence location Cubes are also found in various fields of natural science and technology. It is applied to the unit cell of a crystal known as a cubic crystal system. Table salt is an example of a mineral with a commonly cubic shape. Pyrite has the same shape as well, although there are many variations. The radiolarian Lithocubus geometricus, discovered by Ernst Haeckel, has a cubic shape. A historical attempt to unify three physics ideas of relativity, gravitation, and quantum mechanics used the framework of a cube known as a cGh cube. Cubane is a synthetic hydrocarbon consisting of eight carbon atoms arranged at the corners of a cube, with one hydrogen atom attached to each carbon atom. The bold sentence seems out of place ... better in following paragraphs? The green paragr seems to be listing places where cubes are found in nature. The following paragraphs describe situations where humans analyzed a cube or applied the cube shape to nature (to explain/understand nature).
I consider the second paragraph as a section that includes natural science and its concept. Previously, the technological cube was merged into the same paragraph before someone broke in. Dedhert.Jr (talk) 10:56, 25 September 2025 (UTC)[reply]
Lead wording Other related figures involve the construction of polyhedra based on a cube, space-filling and honeycombs, and polycubes, as well as cubes in compounds, spherical, and topological space. "Figures" does not seem broad enough to encpass all items in the following list. Either (a) break into a few sentences with separate thoughts; or (b) change "figures" to a broader term (but that may be impossible .. "uses" or "applications" or "attributes" do not work). I cannot think of a way to reword that sentence to be sensible, since the listed items are so disparate.
See also section: Consider changing Squaring the square's three-dimensional analogue, cubing the cube to Cubing the cube - Squaring the square's three-dimensional analogue "Cubing the Cube" is key, and should be at the start. I understand the cube material is a section within the Square article, but that could change in the future ... imagine if "Cubing the Cube" became its own article some day in the future ... editors should not need to come back and edit the Cube article.
Wording: Instead, this problem could be solved with folding an origami paper by Messer. (a) Should "could be" be "was". (b) "Instead" doesn't sound ideal. Maybe "However" or omit the word "Instead" entirely.
Sections should start with intro/understandable/fun facts first, then move to advanced/boring topics: "Space Filling" section begins Hilbert's third problem asks whether every two equal-volume polyhedra can always... Better for readers is to start with material they will understand (such as "Cubes are space-filling shapes"). Starting with "Hilbert ..." will cause many readers to bail out of the section.
There is a sidebar InfoBox at the bottom: Template:General geometry. It looks odd, lots of white space to its left. Wouldn't the horizontal navBar Template:Geometry look nicer and be consistent with the conventional WP article layout? Also, the horiz NavBars are collapsible.
A cite-check tool is showing an error on cite Akiyama, Jin; Matsunaga, Kiyoko (2015). "Treks Into Intuitive Geometry". Springer Tokyo: 382–388. doi:10.1007/978-4-431-55843-9. ISBN 9784431558415. MR 3380801. The error says that it is using "cite journal" but the source is a book.
Properties section: first sentence is confusing because it acts like the article is about "cuboids" A cuboid is a polyhedron that consists of six quadrilateral faces... Better is to start with "cubes" in that section then move onto cuboids. Yes it is true that they are all related: general to special: POlyhedron -> Cuboid => Rect Cuboid -> Cube. But readers will want the "Properties" section to _start_ with cube then go from there. Something like: A cube is a polyendron with six square faces, each the same size. A cube is a special form of the more general cuboid, which is ...
For a cube whose circumscribed sphere has radius R , and for a given point in its three-dimensional space with distances di from the cube's eight vertices, it is... The wording is very confusing: it ends with "it is:" which is not good. And it is not clear there are eight "di". Consider If a cube's circumscribed sphere has radius "R", and if any point "P" in 3D space is selected, then the eight distances (d1, d2, ... d8) from P to the eight corners of the cube satisfy the following relation: ...
[continuing from prior] Also: is this formula important? Does this formula have a name? Was is discovered by someone famous? Is it controversial? Do multiple 2ndary sources comment on it? I don't doubt it is a correct formula, but there must be 300 bizarre formulas about cubes ... the article should only include ones that multiple source talk about. If any sources say why this formula is noteworthy, that should be included.
Clarify: The polycube is a polyhedron in which the faces of many cubes are attached. Could this be reworeded to paint a better picture in the reader's mind?
@Noleander. Reworded the cube introduction, as suggested by @RoySmith. The formula about "a cube whose circumscribed sphere has radius ..." is not widely recognized in many sources; if it is, there could be a name for the formula, probably not always. Anyway. I have removed. I'll do the polycube section later because of my busyness recently. Dedhert.Jr (talk) 01:37, 1 October 2025 (UTC)[reply]
Grammar/wording of section title: Polyhedra's construction - That possessive looks (and sounds) really odd. Consider Constructing polyhedra or Construction of polyhedra or Polyhedra that can be constructed from a cube or something like that.
Sections logical? Under section Related figures are subsections Space-filling and Miscellaneous But "Space filling" is not a "related figure" is it? Nor are some of the topics within "Miscellaneous" section. Consider either: (a) Changing the section titles (e.g. change "Related figures" to "Other" or "Miscellaneous"; or (b) raise sections "Space filling" and "Miscellaneous" sections to to top-level (peers of "Related figures") and leave other sections as-is.
The article is slowly approaching FA quality ... not quite there yet, but getting there!
I'm still seeing significant issues with the article, such as:
The cube can be constructed with six square pyramids, tiling space by attaching their apices. In some cases, this produces the rhombic dodecahedron circumscribing a cube. The first sentence is clear: putting 6 square pyramids together produces a cube. I do not understand what the second sentence is trying to say.
Constructing info spread out? There is a section "Constructions" which has "... a cube may be constructed using the Cartesian coordinate systems. ...". But then a similar fact is in a different section: The cube can be constructed with six square pyramids,... why arent those in the same section?
This sentence seems inaccurate: Cubes are space-fillings, where the phrase "space-filling" can be understood as a generalized tessellation. A cube is a "Space-filling polyhedron", not a "space filling". The latter is the result when an infinite number of cubes are assembled together to fill space. The article links "space-filling" to Space-filling polyhedron and so equates the two notions in a confusing way.
... I could find more issues ...
I must reluctantly Oppose. It is a fine article, and a lot of hard work has gone into it ... definitely GA quality.. almost FA quality. I'm still finding issues comparable to those I encountered five weeks ago in my first pass thru the article. I agree with a comment by FA coordinator (below): this "feels more like a PR than a FAC". The nominator has been doing excellent work on the article, and it is gradually getting better!!! Noleander (talk) 14:32, 31 October 2025 (UTC)[reply]
The article generally has many images relative to its length - not sure all are warranted.
Drive-by comment: I don't think we should be applying numerical limits to images based on article length, but rather evaluating them per MOS:IMAGEREL's requirement that they be significant and relevant in the topic's context. Geometry articles are going to be inherently image-heavy because that's often the best way to present a given concept. That being said, I could see trimming some of the images in Appearances (Skewb and Alamo are largely redundant with the die) and I don't think File:Partial cubic honeycomb.png is adding much. RoySmith(talk)12:05, 24 September 2025 (UTC)[reply]
I will give my opinion about this. It depends. If the article is about a specific polyhedron, then yes, we need to provide numerous illustrations of its shape that can be observed in real life. But that does not mean we have to include all of the images corresponding to the list of applications and/or appearances. Dedhert.Jr (talk) 10:48, 25 September 2025 (UTC)[reply]
Good to see this here. I had a quick look around for more things that maybe could be added?
pp. 111–112 of this encyclopedia has a few interesting facts about subdividing cubes with planar cuts, which I don't think is currently in the article.
@AirshipJungleman29. The fact that "cubing the cube" has nowhere to be found in some Google Scholars or Google Books, basically leaving the name only in sources without defining it. I will onhold this topic for now.
Replying to other cube concepts: We don't have an article for Guildford's cube, and it might be helpful for someone to create one. CubeSats already existed in the beginning. The rest are mostly cuboids, as far as I'm concerned. Dedhert.Jr (talk) 01:25, 26 September 2025 (UTC)[reply]
Update: Guildford's cube added. But apparently, I have no knowledge of understanding psychology, especially when I was giving up on searching for the perfect articles for wikilinks, representing those mental factors. Copyedit may be appreciated. Dedhert.Jr (talk) 02:20, 26 September 2025 (UTC)[reply]
One of the problems with a wide-ranging subject like this is figuring out how to interpret WP:FACR's mandate to "neglect no major facts or details". At some point you need to figure out where to draw the line between "major facts" and "details". One could reel off an almost endless string of possible "might be worth discussing" things: Turner's Cube, Cobalt Qube, Bullion Cube, Ice Cube, Cubic Curve, CubeSmart, etc, but that doesn't mean all of those are worth mentioning. RoySmith(talk)02:41, 26 September 2025 (UTC)[reply]
Maybe not all things can be included. Forgot to which MOS stated it similarly. For temporarily, I could rely on some books and journals to include uranium cubic for nuclear program and CobaltQube. Dedhert.Jr (talk) 01:41, 27 September 2025 (UTC)[reply]
My apologies for being unclear, but I wasn't actually suggesting that any of those be included. They were all just examples of thing which on the surface appear to be cube-related but wouldn't pass the bar as a major fact or detail. RoySmith(talk)03:44, 27 September 2025 (UTC)[reply]
Beautifully illustrated. Thanks for such a complete description of something so simple! My main suggestion is to do a good rethink of the lead section. I imagine most readers will not understand a majority of the sentences there. Per WP:EXPLAINLEAD, it should be understandable to a broad audience, which, in this instance, includes the youngest readers we can write for without sounding like we write for children (like 15-year olds without any maths background). —Femke 🐦 (talk) 21:12, 2 October 2025 (UTC)[reply]
This will be the first time commenting on a FAC. I wanted to help review the lead per WP:EXPLAINLEAD since Femke mentioned above that they are Too ill to do things that require brains atm, unfortunately to look over the lead again following changes by the nominator. I have experience giving feedback on technical math articles from some GA reviews (one of which I've done as a reviewer), so I hope what I have to give will be helpful for the article's path to FA. Gramix13 (talk) 01:26, 10 October 2025 (UTC)[reply]
I think the second paragraph, focusing on the cultural occurrences of the cube, should be the last paragraph of the lead so that we can focus first on the mathematical properties of the cube first before discussing its wider applications. There is some wording in this paragraph, while unrelated to being technical, could use some improvement:
The appearance of the cube Remove the phrase "The appearance of" as its a bit too wordy here and I think just saying "The cube" will get the point across more clearly to the reader.
...is found in many popular cultures I feel like the word "popular" should be removed as I think the cube is universal enough to be applicable beyond popular culture, but I also recognize that this article has a section titled Cube § In popular cultures which might be where this wording comes from. I'm open to other commenter's thoughts on this.
Cubes may also be found in Replace "may also" with "can".
It is also found in other antiquity texts Remove "other" since only one text is actually mentioned in the lead.
A cube with 1 side length I would replace "1" with "unit" because "1 side length" makes it sound like there is only a single side and is less clear than a "unit side length".
A cube is a parallelepiped, with pairs of parallel opposite faces with the same shape and size, and a rectangular cuboid with right angles between pairs of intersecting faces and pairs of intersecting edges. I don't like the use of the terms parallelepiped and rectangular cuboid in the lead as I don't think most readers will know what those mean, I'd like to avoid this jargon in the lead. I think we could rephrase the sentence as follows: "Each face of the cube is parallel to a face of the same size on the opposite side of the cube, and adjacent faces are at right angles to each other."
Transformation of a cube includes rotation and reflection between two vertices, two edges, and two faces, which maintains its appearance A bit more wordy and vague than I'd like. I might reword as "The cube can be rotated or reflected about two vertices, two edges, and two faces while maintaining its appearance".
hence, a cube is a regular polyhedron I don't see how the rotation/reflection invariance of the cube implies that it has to be a regular polygon. It would make more sense to remove this and instead mention the regularity in the last sentence of the first paragraph in the lead.>
A cube can be attached with its copy to fill a space without leaving a gap, which forms a honeycomb While technically correct, I think we should leave out the term honeycomb as the reader, without looking at the link's destination, might erroneously confuse this with the hexagon tiling colonially known as a honeycomb.
A cube is part of many classes of space-filling, such as a parallelohedron, plesiohedron, and zonohedron. I think you mean to say space-filling polyhedron before the comma in that sentence. I don't think it's helpful in the lead to mention those three classes of space-filling polyhedron since they're not well-known terms the reader would be aware of.
I struck out most of my comments above since they're no longer relevent in the currerent version of the article, but I did have an additional comment about the first sentence to the third paragraph: Many polyhedra are associated with other polyhedra, which relates to construction based on a cube and represents other geometrical shapes. I feel like this sentence is a bit too vague and unclear. If I understand it correctly, I think its trying to say how the cube can be used to construct other shapes or polyhedron. Mentioning other constructions aside from the space filling honeycomb (which should still have its name removed to avoid confusion) would be helpful for the paragraph. Gramix13 (talk) 19:40, 12 October 2025 (UTC)[reply]
@Gramix13. Okay. I spitted it out the construction. But for the other geometrical shapes, it may refer to shapes that can be included someday. Struggling to find it approachable more specifically nowadays, does reader understand what spherical polyhedron and topological space are? I could have added "magic cube" in some future edits, although changes in the lede may required. Dedhert.Jr (talk) 02:06, 14 October 2025 (UTC)[reply]
Keeping this to a high-school geometry student per RoySmith's suggestion, I'd say topological space would definitely not be expected from the reader, that's a higher level undergraduate topic. I feel like such a student might be able to understand spherical polyhedron with a short explanation, but I think its safe not to include that to be safe.
I'd probably also remove compound, and miscellanea from the third paragraph, since it's not elaborated on what either of those two mean, and I think truncation and attaching should hopefully be sufficient here as the lead. Gramix13 (talk) 03:16, 14 October 2025 (UTC)[reply]
@Gramix13. When I'm trying to say miscallanea, I meant other ways to construct from a cube results in a new kind of polyhedra, other than the first two. I guess this sounds complicated rather than spellbinding. Two examples (truncation and attachment) added only. Dedhert.Jr (talk) 04:51, 14 October 2025 (UTC)[reply]
To be a bit more clear, my issue with "miscellanea", apart from not really being a common English word, is that it teases that there are other ways to assemble polyhedral without explain what they are. The way its written now is much better by directly avoiding that tease, I might add perhaps "by" after "such as" as a small change of grammar. Gramix13 (talk) 05:08, 14 October 2025 (UTC)[reply]
The only two sentences I would keep in the fourth paragraph are A cube with unit side length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured. Many polyhedra are constructed based on a cube. Most of the paragraph uses more technical terms, like Cartesian product of graphs, hypercube, polytopes, and three-dimensional torus. The last term there also runs the risk of confusion with a typical torus which resides in three-dimensional space. This sentence could be merged to the previous paragraph if it cannot be expanded upon.
This concludes my comments about the lead, it is on the way to being understandable to as large of an audience as we can, and hopefully some of my suggestions here help with that goal. Gramix13 (talk) 02:21, 10 October 2025 (UTC)[reply]
I edited my comments above about paragraph 3 since the copy edit, although I don't see much change on paragraph 4 since I wrote my comments. Gramix13 (talk) 19:43, 12 October 2025 (UTC)[reply]
This has been open for more than five weeks and while it has attracted a lot of comments there is only a single declaration of support; in some ways it feels more like a PR than a FAC. Unless it attracts considerable movement towards a consensus to promote over the next two or three days I am afraid that it is liable to be archived. Gog the Mild (talk) 19:25, 28 October 2025 (UTC)[reply]
The term "Kaaba" translates literally to "The Cube". It seems strange to not mention one of the most culturally important "cubes" in history, on the basis that its not technically a perfect cube. – Farkle Griffen (talk)18:34, 16 October 2025 (UTC)[reply]
This is like saying a go board isn't a square grid on a square board, because the board and grid is typically slightly oblong to compensate for the expected viewer perspective. The Kaaba can definitely be called a "cube". –jacobolus(t)18:46, 16 October 2025 (UTC)[reply]
@Jacobolus. If that's the case, I'll added the alongside the architectural building that we have discussed at that time. But do you think "popular culture" is a good spot? Dedhert.Jr (talk) 02:30, 17 October 2025 (UTC)[reply]
level-4 vital article is rated GA-class on Wikipedia's content assessment scale.
Holy cube. What a dope opportunity for DYK to have to showcase this article. Was just recently improved to GA status, so it clears new enough criteria. That GA status also presumably allows for the article (and hook) to clear long (or for hook, short) enough, well-sourced, and presentable criteria. Can confirm after doing a quick double-checking of that on my end. QPQ does not apply here. ALT0 is good to go, but given the scope of the article and the plentiful amount of great images on it, I would definitely support any ALT hooks being developed here. As a result, this is a potential image+hook candidate for the DYK section too. For sure good job on this. Soulbust (talk) 12:44, 7 July 2025 (UTC)
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