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The following is an archived discussion of a featured article review. Please do not modify it. Further comments should be made on the article's talk page or at Wikipedia talk:Featured article review). No further edits should be made to this page.

The article was removed 07:41, 23 January 2007.

Regular polytope

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Review commentary

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I have notified Wikipedia:WikiProject Mathematics / Fred-Chess 22:58, 21 December 2006 (UTC) Message left at Mike40033. Sandy (Talk) 23:30, 21 December 2006 (UTC)[reply]

This article has the same problem as some other older Math FA:s -- they do not contain any inline references. I hereby make a test to see whether Wikipedia's increased demands for FA apply to those articles. I understand that articles on Math are often not perceived as requiring inline citations to such a great extent, but this article contains large sections of history that I think would need inline citations in any other article. Even Wikipedia:Scientific citation guidelines now recomends inline references, even if they appear to be of a different kind than for other articles. / Fred-Chess 22:49, 21 December 2006 (UTC)[reply]

The structure of this article (Layout, MOS, External links, See also, etc.) looks very clean relative to some of the older FAs that come through, and the article looks to be in good shape. The References could benefit from having ISBNs added to the books, and the online reference (Haeckel) should be fully expanded and include a last access date. There are some external jumps (imbedded links) which should be fixed. It looks like adequate reference sources are given so that citing the article shouldn't be too difficult, and there are some inline, Harvard style refs already in place. This article should be salvageable, but I'd sure hate to the one who had to work on it over the holidays :-) Sandy (Talk) 23:39, 21 December 2006 (UTC)[reply]
Seems to have a fair number of Harvard style inline cites, I count 17 in the text. --Salix alba (talk) 23:41, 21 December 2006 (UTC)[reply]
Yes, *embarrassed* , I notice that it used the Harvard referencing. I withdraw my objections. / Fred-Chess 23:51, 21 December 2006 (UTC)[reply]
It doesn't need to be withdrawn: with a minimum amount of work, it could be a nice Save/Keep. There were Harvard citations, but not thorough or complete (I've now converted them to cite.php .) The external jumps and inline URLs need to be dealt with, and there are still some statements that do need to be cited. If anyone is willing to work on it, I can add cite tags. Also, some of the inlines that were there aren't specific (page nos). There are also some minor prose issues which should be cleared up (example: "Cayley gave them English names which have become accepted. They are: (Kepler's) the small stellated dodecahedron and great stellated dodecahedron, and (Poinsot's) the great icosahedron and great dodecahedron.") If someone could comb through it, it could be closed as a successful FAR. Sandy (Talk) 03:21, 22 December 2006 (UTC)[reply]
I converted most of the external jumps to notes, and cleaned up See also, which contained articles already linked in the text. I saw a lot of copyediting needs in the article - unencylopedic commentary and sentence fragments - in addition to the statements needing citation. I hope someone else will comb through it - it's not in bad shape, but if we could complete the work, it can be taken off of the list of articles with citation needs. Sandy (Talk) 04:05, 22 December 2006 (UTC)[reply]
You've been reverted.--Rmky87 20:53, 24 December 2006 (UTC)[reply]
They can use whatever style they want, but the article is still undercited, some of the references are incomplete, there are prose issues, and there are imbedded links to external websites (which should be either wikified or converted to a reference). And, since all of my work was reverted, the article now needs attention to wikilinking, consistency in capitalization of platonic, and See also cleanup (for articles already linked in the text). If someone reverted, the good news is that the article is not abandoned like most older FAs, and maybe the necessary cleanup, polishing and referencing will happen. Sandy (Talk) 06:06, 25 December 2006 (UTC)[reply]

List (entirely random - there's much more - these are samples only):

  • Fix blue link on Haeckel reference, and provide last access date.
  • It would be nice if the references had ISBNs
  • Platonic solids - sometimes capitalized, sometimes not, linked throughout the article, but then listed again in See also. (In other words, all Wikilinking should be reviewed.)
  • H. S. M. Coxeter and List of regular polytopes linked in article, yet re-listed in See also (I had corrected items like this, my changes were reverted).
  • History is largely uncited. The introduction to history could use some variety in the choice of words (wide and gradual): "The history of discovery of the regular polytopes can be characterised by a gradual broadening of widespread understanding of the term. Gradually, the term "regular polytope" has been given successively wider meaning, allowing more different geometric objects to be so labeled. With each widening, new geometric figures are uncovered — these new figures usually being completely unknown to previous generations."
  • (A sample of uncited, weasle words, as well as poor prose style, sending Wiki readers "elsewhere in the article") It may be argued, however, that the construction of this form was inspired by the pyritohedron (mentioned elsewhere in this article), as pyrite minerals are relatively abundant in that part of the world.
  • The entire next paragraph, beginning with "Preceding even the Etruscans" is uncited, contains an imbedded link to a room in a museum, and a throw-away sentence ("It is impossible to know why these objects were made, or how the sculptor gained the inspiration for them.")
  • (The next sentence in history is unreferenced, and weasly) There is no existing evidence that the Etruscans or ancient Scots had a mathematical understanding of the regular solids — nor is there any proof that they did not. The discovery of the three-dimensional polytopes, particularly of the simpler ones, is probably impossible to trace.
  • (This section is referenced, but a snake for the chopping.) Some authors (Sanford, 1930) credit Pythagoras (550 BC) with being familiar with the Platonic solids, whereas others indicate that he may only have been familiar with the tetrahedron, cube, and dodecahedron, crediting the discovery of the other two to Theaetetus (an Athenian), who in any case gave a mathematical description of all five (Van der Waerden, 1954), (Euclid, book XIII). H.S.M. Coxeter (Coxeter, 1948, Section 1.9) credits Plato (400 BC) with having made models of them, and mentions that one of the earlier Pythagoreans, Timaeus of Locri used all five in a correspondence between the polyhedra and the nature of the universe as it was then perceived - this correspondence is recorded in Plato's dialogue Timaeus.
  • (Moving further down in history, another throw-away, filler sentence.) More have been discovered since, and the story is not yet ended.
  • (Still in history, whose opinion is this?) The latter reference is probably the most comprehensive printed treatment of Schläfli's and similar results to date.
  • (Still in history - spot the redundancy) This concept may be easier for the reader to grasp if one considers the relationship of the cube and the hemicube.
  • (Moving out of history - interesting prose): (One could ask the same question about the polygons, of course.) ... The English word "construct" has the connotation of systematically building the thing constructed.
  • (Samples of unencylopedic, weasly prose, linking to external website): Some interesting fold-out nets of the cube, octahedron, dodecahedron and icosahedron are available here. ... In theory, almost any material may be used to construct regular polyhedra. Instructions for building origami models may be found here, for example. They may be carved out of wood, modeled out of wire, formed from stained glass. The imagination is the limit.

In short, Fred has no need to be embarrassed for nominating this article for review: references and prose need work throughout - these are samples only. Sandy (Talk) 06:57, 25 December 2006 (UTC)[reply]

I agree with all of Sandy's comments about the lack of citations and vague prose. I have a few additional comments.
  • Whenever the article claims that regular polytopes had a particular definition at some moment in time it should provide a reference to a source who uses or describes that definition. I doubt that the Greeks had any definition for the phrase regular polytope; the article implies that they did. What seems to be true is that the regular polytopes include the polygons and polyhedra known to the Greeks.
  • If this is a math article, it should be edited to meet the spirit of the scientific citation guidelines. In particular, the article does not explicitly point out a general reference, and many sources are omitted.
  • The references section should be edited to agree with the examples at WP:HARVARD.
CMummert 13:40, 27 December 2006 (UTC)[reply]

FARC commentary

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Suggested FA criteria is lack of citations (1c). Marskell 19:07, 7 January 2007 (UTC)[reply]
  • Keep I agree that the handful of historic speculations should be removed; in fact, I'll go remove them; but they are marginal to the article anyway. As for Coxeter's book: it is the standard work on the entire subject, and anything else which is uncited is almost certainly sourced there; this is therefore unlikely to be challenged by anyone who has actually looked at the listed sources: I would be surprized if most of them, taken at random, do not support this characterization. I see no other flaws that amount to lack of clear citation for challengeable assertions. Septentrionalis PMAnderson 15:36, 9 January 2007 (UTC)[reply]
    • I removed some speculation. Both the discoveries in Tuscany and in Scotland are sourced; I left an assertion that the purpose or intent of non-functional prehistoric artifacts is unknowable, as both obvious and a useful reminder to our more non-conventional readers.Septentrionalis PMAnderson 15:43, 9 January 2007 (UTC)[reply]
      • I suggest a thorough read of the article, and the list of issues discussed on review, most of which have not been addressed in any significant way. Your edit to one paragraph addressed a miniscule part of the list of issues. (And please don't tell me to do the work - I started on it, and my work was reverted.)
      • It shouldn't be too hard to clean up the See also, fix the wikilinking, and decide whether you all want to capitalize things like platonic solids or not - I already did that sort of work once, and my corrections were reverted - it's not really rocket science, but someone needs to do the work.
      • I'm wondering if the Math Project considers these to be samples of brilliant and compelling prose and good referencing worthy of FA status? I suggest that editors complaining about other areas of Wikipedia that count cites should at least read an article before defending it.
        • Brilliant and compelling - I don't believe Britannica or textbooks routinely send their readers to [1] to read up on topics. Also, 1b would indicate we shouldn't be sending our readers to external jumps anyway; for an article to be considered comprehensive, we should write the text ourselves and reference or link to it:
          • For example, the fold out nets mentioned in the previous section have higher-dimensional equivalents. Some of these may be viewed at [1].
        • Choppy, compelling and brilliant external jumps :
          • Such a tessellation forms an example of an infinite abstract regular polytope. An example may be seen at this page.
          • Other examples may be found on the web (see for example [2]).
        • Here are my two favorite examples of this article's encyclopedic, brilliant and compelling prose:
          • For a given polyhedron there may be many fold-out nets. For example, there are 11 for the cube, and over 900000 for the dodecahedron. Some interesting fold-out nets of the cube, octahedron, dodecahedron and icosahedron are available here. (Reminder to check WP:MOS for usage of commas in 900000.)
          • In theory, almost any material may be used to construct regular polyhedra. Instructions for building origami models may be found here, for example. They may be carved out of wood, modeled out of wire, formed from stained glass. The imagination is the limit.
        • Does this add to the wealth of encyclopedic knowledge on the topic (is it an advert?) Such models are occasionally found in science museums or mathematics departments of universities (such as that of the Université Libre de Bruxelles).
        • Encyclopedic tone? In this way, we can see (if not fully grasp) the full four-dimensional structure of the four-dimensional regular polytopes, via such cutaway cross sections. and One might even imagine building a model of this fold-out net, as one draws a polyhedron's fold-out net on a piece of paper. Sadly, we could never do the necessary folding of the 3-dimensional structure to obtain the 4-dimensional polytope, because of the constraints of the physical universe.
        • Choppy prose The outer protein shells of many viruses form regular polyhedra. For example, HIV is enclosed in a regular icosahedron.
        • Hypothesized sounds weasly, should say by whom Although C60, the most easily produced fullerene, looks more or less spherical, some of the larger varieties (such as C240, C480 and C960) are hypothesised to take on the form of slightly rounded icosahedra, a few nanometres across.
        • "As an aside"? (Entire paragraph uncited as well.) As an aside: In ancient times the Pythagoreans believed that there was a harmony between the regular polyhedra and the orbits of the planets.
        • Compelling, and truly encyclopedic prose: Kepler's work, and the discovery since that time of Uranus, Neptune and Pluto, have thrown the Pythagorean idea well and truly into the dustbins of scientific history.
        • More compelling brilliant prose - the world of minerals? In the world of minerals, crystals often have faces which are triangular, square or hexagonal.
        • "Fascinating" is encyclopedic prose? Another fascinating example of regular polygons occurring as a result of geological processes may be seen at the Giant's Causeway in Ireland, or at the Devil's Postpile in California, where the cooling of lava has formed areas of tightly packed hexagonal columns of basalt.
        • Honeycomb is "famous"? The most famous hexagons in nature are ...
        • Passive voice, missing punctuation, then a snake, followed by choppy prose. There also exist animals who themselves take the approximate form of regular polygons (or at least have the same symmetry) for example starfish and sometimes other echinoderms (such as sea urchins) display the symmetry of a pentagon or sometimes other polygons (such as the heptagon). In fact, echinoderms do not display exact radial symmetry. However, Jellyfish and Comb jellies do, usually fourfold (like the square) or eightfold.
        • More brilliant prose, a type, and choppy parenthetical writing: Moving off earth into space, early mathematicians doing calculations using Newton's law of gravitation discovered that if two bodies (such as the sun and the earth) are orbiting one another, there exist certain points in space where a smaller body (such as an asteroid or a space station)will remain in a stable orbit, following (for example) the earth but never catching up or falling behind.
        • Choppy, disjointed prose. These points are called Lagrangian points. The sun-earth system has five Lagrangian points. The two most stable are exactly 60 degrees ahead and behind the earth in its orbit. That is, joining the centre of the sun and the earth and one of these stable Lagrangian points forms an equilateral triangle. Astronomers have already found asteroids at these points.
        • Brilliant. Cite needed on weasle, and an exclamation point to round out the encyclopedic tone. It is still debated whether it is practical to keep a space station at the Lagrangian point — although it would never need course corrections, it would have to frequently dodge the asteroids that are already present there! (Already there are satellites and space observatories at the less stable Lagrangian points, which do not form the point of an equilateral triangle with the earth and the sun.)
        • Of course - I encounter "of course" all the time in encyclopedias and textbooks. Of course reasonably accurate approximations can be constructed by a range of methods; while theoretically possible constructions may be impractical.
      • That's only a few sections at the bottom. Rather than continue, I'll skip back to the top to see if it has improved yet.
        • I see we still have this piece of gradual-broad-wide-gradual-wide-wide brilliance: The history of discovery of the regular polytopes can be characterised by a gradual broadening of widespread understanding of the term. Gradually, the term "regular polytope" has been given successively wider meaning, allowing more different geometric objects to be so labeled. With each widening, new geometric figures are uncovered — these new figures usually being completely unknown to previous generations.
      • I'll stop there. Please fix the prose, finish referencing, correct the wikilinking and ce issues, and remove the external jumps. Per 1b, please wikify text, and link to it internally or via references. Is this really work the Math Project is proud of and wants to display as an example of Wikipedia's best work in Math? SandyGeorgia (Talk) 17:49, 9 January 2007 (UTC)[reply]
  • Comment -- the concerns presented above seem to me to have varying degrees of validity, as far as the featured status of the article goes. I've corrected some issues and will try to undertake some more; however, some of Sandy's complaints I don't quite see the thrust of (honeycombs aren't famous?; what's wrong with fascinating; etc.) And the external jumps, though I haven't checked them all, appear to be useful and quite valuable. Although we may have to agree to disagree on that. Christopher Parham (talk) 22:17, 15 January 2007 (UTC)[reply]
    • External jumps discussed at Wikipedia:Featured article review/Monty Hall problem (Curiously silent section). It's not that the info in the jumps isn't useful or shouldn't be included: if it should be included, and it's not Wikified, that argues against 1b. We can either Wikify the content (per 1b), or discuss the content, linking to the external site as a reference (WP:NOT and WP:EL), or if we simply must include an external jump in text (e.g.; copyright reasons, and we truly can't write it ourselves), at least the text should conform to 1a, good prose. "Fascinating" is editorializing, not encyclopedic prose, and I can't really add more to the honeycombs as "famous" issue. :-) It would be helpful if the Math Project would get a topnotch copyeditor on board, because neither of these two articles on review are difficult mathmatically; yet, the prose is making the topics appear difficult. SandyGeorgia (Talk) 01:15, 16 January 2007 (UTC)[reply]
      • None of the material that is linked to should be included in this article, as far as I can tell; however it is information that may be helpful to someone who is interested in further examination of the particular topic being discussed. If someone wants to create a new article on Wikipedia about the topic, that would be great, and we could link to that article instead. Until that happens, the external link is the best choice; either way, whether or not that other article has been written shouldn't impact whether this article is featured. If you feel that the text surrounding those links is not good prose, please suggest an alternative. It seems fine to me. Christopher Parham (talk) 03:30, 16 January 2007 (UTC)[reply]

Went back to check only on External jumps (haven't yet checked to see if the extensive list of other problems has been addressed):

  • Examples of these stones are on display in the John Evans room of the Ashmolean Museum at Oxford University. It is impossible to know why these objects were made, or how the sculptor gained the inspiration for them.
    • This text adds nothing to the topic. The second throw-away sentence is still there. Since the link is dead, I'm wondering what value you find in the external jump? I looked it up in the internet archive, and even if the link were live, it adds nothing to the topic. [3] The second sentence is a throw-away sentence. I can see no justification for this jump.
  • Euclid's elements (see for example Euclid's Elements) gave what amount to ruler-and-compass constructions for the five Platonic solids.
    • Euclid's elements followed by see Euclid's elements is not good prose. The page demonstrates nothing; it's a collection of links. Editors should write whatever it is they're intending to convey with that link, and use it as a reference. Fails 1a and 1b.
      • The page is the index for directions, accompanied by vector graphics, of the construction of each of the five solids. Obviously these instructions should not be included in the article, but I think they may well be of interest to the reader. I've clarified the prose to indicate what sort of examples are indicated. Christopher Parham (talk) 07:26, 16 January 2007 (UTC)[reply]
  • In theory, almost any material may be used to construct regular polyhedra. Instructions for building origami models may be found here, for example. They may be carved out of wood, modeled out of wire, formed from stained glass. The imagination is the limit.
    • Again, throw-away, speculative sentence still here, no progress apparent in this article. Instructions for building origami models should be found in an origami article - there is no need for an external jump here, and the prose is not unencyclopedic. Would you expect to find "may be found here" when reading the article in hard print? We put external jumps in External links for a reason.
      • Obviously there are many things here that I would not expect to find in a print encyclopedia; in print the link would have to be expanded to include the full URL. Putting this link at the end of the article wouldn't make much sense given that it applies to this sentence in particular. Christopher Parham (talk) 07:26, 16 January 2007 (UTC)[reply]
  • Other examples may be found on the web (see for example [4]).
    • Not defensible. See [4] isn't good prose; we don't need to link out for examples - we can do that in External links or a Wiki article on orthorgraphic projections.
  • Coxeter's famous book on polytopes (Coxeter, 1948) has some examples of such orthographic projections. Other examples may be found on the web (see for example [5]). Note that immersing the 4-dimensional objects directly into two dimensions is quite confusing.
    • Please don't tell readers what to note. "Famous" is unencylopedic. Some is redundant. Other examples can be included in External links. See [2] fails 1a. Quite is redundant. Again, the math here isn't the issue: it's the tortured prose and the insistence on the use of external jumps and convoluted referencing that makes the math appear harder than need be. Write plain text, reference it to coxeter and the external site, add the external site to the refs section.
      • This link is a good candidate to be moved to the external links section, since it has general relevance. As far as your comments on the prose go, I don't see what's unencyclopedic about "famous" (the book is indeed famous). Christopher Parham (talk) 07:26, 16 January 2007 (UTC)[reply]
  • The mathematics department at UIUC has a number of pictures of what one would see if embedded in a tessellation of hyperbolic space with dodecahedra. Such a tessellation forms an example of an infinite abstract regular polytope. An example may be seen at this page.
    • What is this section doing (or trying to do); it adds nothing but an advert for Champaign-Urbana. Why does the reader care about the Math dept at UIUC? Write the text without referring to the math department, say it simply, reference the site inline with a link in refs.
  • I could go on - but I can see that nothing has yet been done to bring the article to standard. It fails 1a, and probably still 1b and 1c as well. The problem here is not only the lack of citations (of which there is still plenty in this article); it's the poor prose making the math appear harder than need be, made even more difficult by too much of the prose being about the source, rather than using the source only to reference facts. It's time to stop waving arms about citations and assuming others don't understand the math: this article is simply poorly written. SandyGeorgia (Talk) 06:07, 16 January 2007 (UTC)[reply]
    • Generally, links like these need to be evaluated on an individual basis. But certainly I think your standards for inclusion are unreasonably narrow. As far as the article needing a copyedit, I don't disagree; if I get a chance to do it to my satisfaction, I will. Christopher Parham (talk) 07:26, 16 January 2007 (UTC)[reply]
  • Remove Insufficient inline citations. LuciferMorgan 02:31, 20 January 2007 (UTC)[reply]
  • Remove as per Lucifer. And it's not well written at all. When the citations issue is addressed, consider asking the LoC.
    • "because they do not have plane faces"—Just "lack". It's a complicated topic for non-experts, so attention to clear, plain expression is essential.
    • Please don't use "indeed" in an encyclopedic register. What does it mean?
    • "Overall, however, the history of the study of regular polytopes has been one where the definition has been steadily generalised, allowing more and more objects to be considered among their number." At first glance, elegant. A few seconds later, you realise that it's flabby. Be straight, plain and concise for us poor dummies. Remove the thematic equative "the history [equals] one where ...". "Among their number" is redundant, as is "of the study". Try: "Since Euclid, the definition of regular polytopes has been gradually expanded to include more objects." How simple is that, now?

These examples from the top indicate that the whole text requires careful attention by fresh eyes.Tony 00:00, 21 January 2007 (UTC)[reply]

The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article review. No further edits should be made to this page.
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