Talk:Triaugmented triangular prism

Triaugmented triangular prism has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: December 9, 2022. (Reviewed version).

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GA Review

Passed. Etrius ( Us) 02:37, 9 December 2022 (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.

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

Reviewer: Dedhert.Jr (talk · contribs) 12:32, 25 November 2022 (UTC)[reply]

Hi. I will be reviewing this article. This is the first time I review it, so there is a chance that I will require a second opinion. I will try my best, although my English is not excellently professional. Dedhert.Jr (talk) 12:32, 25 November 2022 (UTC)[reply]

I am still warming up, so I can only give this:

"A triaugmented triangular prism is a convex polyhedron with 14 equilateral triangles as its faces", while "tetrakis triangular prism, tricapped trigonal prism, etc. means that a polyhedron with 14 triangular faces". Umm, is there any between the equilateral and triangular faces? I can only know that the "equilateral" means the same sides of a triangle, but I have no idea about what "triangular" means in this context. Does it mean it is some kind of arbitrary side of a triangle, i.e., scalene? Dedhert.Jr (talk 12:37, 25 November 2022 (UTC)[reply]

#Construction: "When a polyhedron has only equilateral triangles as its faces, like this one, it is called a deltahedron." What do you indicate here as you write the phrase "like this one"? Dedhert.Jr (talk) 12:46, 25 November 2022 (UTC)[reply]

#Fritsch graph It was used by Fritsch & Fritsch (1998) as a small counterexample to Alfred Kempe's false proof of the four color theorem using Kempe chains, Small counterexample? Would you like to explain what this means? Dedhert.Jr (talk) 12:53, 25 November 2022 (UTC)[reply]

I can't find Soifer graph on a search. Perhaps it is not created at all. Dedhert.Jr (talk) 12:53, 25 November 2022 (UTC)[reply]

Triangular means shaped like a triangle. The faces are triangles. Their shape is triangular.

Like this one = like the triaugmented triangular prism.

Re "Would you like to explain what this means?": like everything in the lead, the detailed explanation is later. In this case, "later" means in the caption of the illustration in the "Fritsch graph" section.

We do not have an article on the Soifer graph. Nevertheless, that phrase has been used in the mathematical literature. About 18 times, according to Google Scholar. —David Eppstein (talk) 19:43, 25 November 2022 (UTC)[reply]

Re:Re:"Would you like to explain what this means?": I mean, what is the meaning of "small counterexample" anyway? I can only understand "counterexample" meaning, but I've never heard of the adjective word "small". My apologies if I still didn't catch it at all. Dedhert.Jr (talk) 00:16, 26 November 2022 (UTC)[reply]

In this case, small means "as few vertices as possible, but there is another one with one fewer edge". This is explained, in the section I pointed to. —David Eppstein (talk) 00:27, 26 November 2022 (UTC)[reply]

Another comments:

#Dual associahedron Is $A_{3}$ means a group here? Dedhert.Jr (talk) 00:19, 26 November 2022 (UTC)[reply]
This is a notation used to classify lots of different types of mathematical objects, including the ones named here. Some of them are groups (more precisely Lie groups). I think it might make the article too technical to go into more detail about how all these different kinds of objects correspond to the 3d associahedron, but each of the linked articles talks about how similar notation is used for the linked topics. —David Eppstein (talk) 00:29, 26 November 2022 (UTC)[reply]
So in conclusion, what does $A_{3}$ means? I think it would more helpful to add an explanation about $A_{3}$ in this particular context. Dedhert.Jr (talk) 00:38, 26 November 2022 (UTC)[reply]
It means "the third thing in the A-series of the classification of this sequence of mathematical objects". It has a different meaning for each type of object, that would be complicated and technical and off-topic to explain in detail. For instance, the A3 Dynkin diagram is a diagram of little circles and lines between them that looks like — there are three little circles, and (unlike some other Dynkin diagrams) the lines are not decorated with numbers. The A means that it is just a straight row of undecorated circles and lines, and the 3 means that there are three circles. That's probably the easiest one to explain but the least helpful in terms of understanding how it relates to the associahedron. —David Eppstein (talk) 00:48, 26 November 2022 (UTC)[reply]

Does it a little bit MOS:SANDWICH between pictures in Fritsch graph and Dual associahedron? Dedhert.Jr (talk) 00:38, 26 November 2022 (UTC)[reply]
I deliberately tried to offset these two images vertically by enough distance so that, if you narrow down your screen width small enough for sandwiching to be relevant, you will also cause the text to spread out into enough more rows that they would be one above the other rather than overlapping. That's what I see when I try it in my browser, anyway. By the time I make it narrow enough for each image to be about 1/3 of a column wide, with 1/3 of a column of text between them, they do not have any rows of text in common with each other. Do you see something different? —David Eppstein (talk) 00:52, 26 November 2022 (UTC)[reply]
Yeah. I see it. But I may have two options for such this case: Maybe you can reorder Fritsch graph and Dual associahedron. If you have any objection, then I suggest using {{clear}}, although it would leave some gaps. Dedhert.Jr (talk) 00:55, 26 November 2022 (UTC)[reply]
{{Clear}} makes

big ugly blank spaces in articles. MOS:SANDWICH says that left-right-facing images should be used with caution because they MIGHT cause problems. They would cause problems for images directly aligned left to right, as in the example in MOS:SANDWICH, but in this article they are not directly aligned and they do not cause any actual problems. Your comment suggests that you are trying to follow rules for the sake of following rules rather than taking the effort to think about what the rules actually mean. Pay more attention to the part of MOS:SANDWICH that says why it makes that suggestion: because that image placement "can create a distasteful text sandwich (depending on platform and window size)". But in this case it doesn't, so the rule is unnecessary and enforcing it is being bureaucratic for the sake of being bureaucratic rather than being in any way constructive. More, it would cause problems (the unnecessary whitespace) rather than actually fixing any problem.

And no, I cannot reorder the sections. Having a tall left image too close to the references section is another way to cause much bigger problems: it screws up the alignment of the columns in the entire references section. —David Eppstein (talk) 01:24, 26 November 2022 (UTC)[reply]
Ah, sorry for that, and I would be more careful in giving suggestions next time. Dedhert.Jr (talk) 01:34, 26 November 2022 (UTC)[reply]

...and the pyramid has dihedral angles of half that of the regular octahedron. "that" in this sentence is indicating the prism, which is inscribed in a $J_{51}$ ? Not quite understand about it. Dedhert.Jr (talk) 01:05, 26 November 2022 (UTC)[reply]
You are reading it wrong. In this sentence "that" stands for "dihedral angles". But I rewrote it to expand that part a little. —David Eppstein (talk) 01:31, 26 November 2022 (UTC)[reply]
Thanks for copyediting. But I still don't get it: The prism itself has square-triangle dihedral angles $\pi /2$ ... . Does "square-triangle" mean both square and triangle faces create a dihedral angle, which is $\pi /2$ ? Aside from it, ...and the square-triangle angles are half that. Umm, what is that again "that" means? Apologies for the second asking. Dedhert.Jr (talk) 01:53, 26 November 2022 (UTC)[reply]
"Dihedral angle" always means the angle between two faces. (Polyhedra also have other kinds of angle: the angles between two edges, or the solid angles at vertices.) Because the polyhedra described here have more than one kind of dihedral angle, we need to clarify which ones we are talking about in some unambiguous way. The way we are doing that is to say what kinds of faces each angle is between. A square-triangle dihedral angle is the dihedral angle on the edge connecting a square to a triangle.

"That" is a pronoun in this context. In general, in English, pronouns refer to the most recent thing mentioned in a previous sentence that might make sense. You are a native speaker of English, right? In this case, the only recently mentioned previous thing that makes any sense is the dihedral angle of a regular octahedron. "Half that" means "Half the dihedral angle of a regular octahedron". —David Eppstein (talk) 20:39, 27 November 2022 (UTC)[reply]

...and on the square-to-square prism edges... "square-to-square prism"? Dedhert.Jr (talk) 01:56, 26 November 2022 (UTC)[reply]
A triangular prism has nine edges. We can call these "prism edges", especially if we want to distinguish them from the edges of some other polyhedron. The prism has five faces: two triangles and three squares. Six of the prism edges connect a triangle to a square. We can call these "triangle-to-square prism edges". The other three prism edges connect a square to a square. We can call these "square-to-square prism edges".

English, do you speak it? Because a large number of your comments here indicate some confusion with basic English grammar rather than with the mathematics in the article. It might be better to improve your skill in this area before diving into Good Article reviewing. —David Eppstein (talk) 20:44, 27 November 2022 (UTC)[reply]

#Dual associahedron: I can see two right parentheses in the first sentence in the second paragraph. Dedhert.Jr (talk) 02:35, 26 November 2022 (UTC)[reply]
Thx, fixed. —David Eppstein (talk) 20:50, 27 November 2022 (UTC)[reply]

#Fritsch graph These six graphs come from the six Whitney triangulations that, when their triangles are equilateral, have positive angular defect at every vertex. This makes them a combinatorial analogue of the positively curved smooth surfaces. Really? How do these graphs can makes them a combinatorial analogue of the positively curved smooth surfaces? And what does "combinatorial analogue" means here? Dedhert.Jr (talk) 04:09, 26 November 2022 (UTC)[reply]
This is getting well beyond the topic of the article, but in general there are close similarities between the integral of the Gaussian curvature of a smooth surface, and the sum of the angular defects at the vertices of a polyhedral surface. For instance, either of these quantities, summed over the whole surface, gives you a number that is related to the Euler characteristic of the surface and unrelated to the way that it bends in any local area (this is the Gauss–Bonnet theorem). You can take any smooth surface and approximate it by a polyhedral surface, concentrating all its curvature at the vertices. Or you can take any polyhedral surface and smooth off its edges and vertices, spreading out the curvature from the vertices to nearby points on the smoothed surface. Neither of these deformations can change the overall total curvature.

For these six graphs, you can make a topological surface (the Whitney triangulation) by gluing together equilateral triangles, in a high-enough dimensional space to allow you to do this without bending the triangles or letting them cross each other. Just make a geometric triangle for each triangle in the graph, and glue together two triangles whenever they share an edge. Every edge is shared by exactly two triangles. Because the sum of the defects is positive, the surfaces formed from these graphs must be topologically the same as smooth surfaces whose integral of Gaussian curvature is positive. The only smooth surfaces whose integral of Gaussian curvature is positive are the topological sphere and the projective plane. However, for these graphs you can only get a sphere, not a projective plane. More strongly, a geometric sphere has positive curvature at every point, not just in total. These graphs have an analogous property: they have positive angular defect at every vertex, not just in total. They are "combinatorial analogues" because their curvature comes only from a finite combinatorial structure (their vertices and edges), without any continuously varying numbers. —David Eppstein (talk) 21:03, 27 November 2022 (UTC)[reply]

#Fritsch graph "the bottom edge in the illustration"? Is the illustration here mean the Fritsch cover book? Dedhert.Jr (talk) 13:08, 26 November 2022 (UTC)[reply]
It means the only illustration in this section of the Wikipedia article. I added "here" to clarify that. Note that Wikipedia's MOS discourages more specific descriptions of image locations like "to the left", in part because on mobile the image will not be to the left. —David Eppstein (talk) 20:51, 27 November 2022 (UTC)[reply]

#Applications ...it is common to visualize an atom cluster surrounding a central atom as a polyhedron—the convex hull of the surrounding atoms' locations. Is the phrase "convex hull of the surrounding atoms" referring to how to visualize an atom cluster surrounding it? Dedhert.Jr (talk) 13:34, 26 November 2022 (UTC)[reply]
A convex hull is a way of constructing a polyhedron from points. It is not itself a visualization, it is a polyhedron. Again, this is an issue of grammar — the phrase set off by dashes is a more detailed explanation of the word "polyhedron" from the main part of the sentence. "The convex hull of the surrounding atoms' locations" is the polyhedron constructed in this way from the points where the surrounding atoms are located. —David Eppstein (talk) 20:53, 27 November 2022 (UTC)[reply]

Thanks a lot for the explanation here, but I think I really need a second opinion. About my native speaker, no, my native is not English. I already mentioned it at the beginning, not excellently professional. My apologies if I continuously ask more questions. Dedhert.Jr (talk) 23:46, 27 November 2022 (UTC)[reply]

@Dedhert.Jr: and @David Eppstein:, I'll take this over. I'll do my best to interpret the notes above.

Copy-vios I ran this through Earwig for posterity's sake, nothing exciting. I hunted down a few of these sources, no close paraphrasing found.
Images Nothing of note
Sources No concerns, all seem reasonably reliable

Prose

First sentence is pushing MOS:LEAD, depending on how dogmatic you want to be. I personally would say "A triaugmented triangular prism, in geometry, is...."
MOS:CITELEAD, I get that most of the footnotes are acceptable in the lead for a page of this technical level but I fail to see how FN 1, which seems to be citing the name itself, is necessary.
a process called augmentation Mention in body, Lead is meant to be a summary
" like this one" clarify
can be derived by slicing it into a central prism and three square pyramids, and adding their volumes I see this is implicity cited by FN 9 but please humor me and add it.

I get that these are mainly nit-picks. The page is very well written overall. User:Dedhert.Jr, don't feel back about the review. Everyone's first review is always a bit rough and there's no right way, besides just trying (hence WP:BEBOLD). I'm a fairly experienced GA reviewer and I've definitely made my share of mistakes (and still do!!!). I'll override and place this on hold if it wasn't already. Once these issues are addressed, I'll gladly pass the article. Etrius ( Us) 02:26, 8 December 2022 (UTC)[reply]

Thanks! I haven't had time yet to address your comments but will soon. They all look like likely improvements at first glance. —David Eppstein (talk) 02:38, 8 December 2022 (UTC)[reply]

@Etriusus: Ok, all done, I think, except that I removed the "like this one" rather than trying to explain it. I also replaced a couple of footnotes to Pugh by footnotes to Trigg, since Trigg better explains the three-pyramid construction and properly sources the "augmentation" terminology. —David Eppstein (talk) 02:27, 9 December 2022 (UTC)[reply]

I reviewed it again, no issues within the scope of GA is present. Article passes, congrats!!!

Good Article review progress box

Criteria: 1a. prose () 1b. MoS () 2a. ref layout () 2b. cites WP:RS () 2c. no WP:OR () 2d. no WP:CV ()

3a. broadness () 3b. focus () 4. neutral () 5. stable () 6a. free or tagged images () 6b. pics relevant ()

Note: this represents where the article stands relative to the Good Article criteria. Criteria marked are unassessed

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.

Sphericity

Should the sphericity be added to this article? The source from Berman already explained it. Dedhert.Jr (talk) 12:54, 25 July 2024 (UTC)[reply]

Okay! —Tamfang (talk) 23:57, 26 July 2024 (UTC)[reply]