Talk:Final stellation of the icosahedron/Archive 1

Archive 1

Notable enough?

Is this polyhedron really notable enough to merit its own article? There is certainly nothing that notable in this article as it stands. -- Cheers, Steelpillow (Talk) 20:42, 31 July 2008 (UTC)

I agree being a redirect is good enough for me. I am curious who named it, but I've never seen an source. Tom Ruen (talk) 21:46, 31 July 2008 (UTC)

I think it merits its own article. It has a specific name, it has its own MathWorld article, and it is the final stellation of the icosahedron. There is information here that will be lost if this page just redirects. As a precedent, we have separate articles for all three stellations of the dodecahedron. Yes, the article is a bit stubby at present, but I can work on expanding it. Gandalf61 (talk) 08:22, 1 August 2008 (UTC)

I can go either way, glad if this can be expaned. The precedent of the dodecahedral stellations isn't as strong since they exists also as star polyhedra. There's also article for the regular compounds which again have a separate construction.

Actually the whole issue of a stellation BEING named a -hedron is problematic to me, since I see a polyhedron as a connected closed manifold surface (2 faces on every edge), while the stellations are something different.

Well, happy editting as far as I'm concerned! :) Tom Ruen (talk) 18:16, 1 August 2008 (UTC)

A stellation may or may not comprise more than one polyhedron (or compound polyhedron). Some stellations are "-hedra" while others are not. I agree that the dodecahedral stellations as a whole are notable, because of their historical development and theoretical importance. However I also feel that the article on the Kepler-Poinsot polyhedra is enough and the individual articles should be merged into it. The echidnahedron has nothing notable about it other than its name, which IMHO is not enough to justify an article. Still, I may be wrong, so I'll wait and see what User:Gandalf61 can dig up. -- Cheers, Steelpillow (Talk) 20:03, 1 August 2008 (UTC)

Tom referred me to this article, so here goes:

• "the final stellation of the icosahedron" — So it is unique within the class? If so, the article could state that explicitly ("final stellation" may be a bit obscure for some readers).

It is the outermost cell set, and hence the end point of the series - just as the core icosahedron is the starting point. Every stellate-able polyhedron has such a final stellation. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

OK. Could you expand stellation with a definition? final stellation is a red link and a WP search does not find the term. I have tagged it here, but realize that an explanation in this article is beyond its scope. --Jtir (talk) 21:36, 2 August 2008 (UTC)

The phrase "final stellation" is used in such an obvious way that defining it per se becomes ridiculous. One might even think of it as, itself, the definition of the end point of the stellation process. -- Cheers, Steelpillow (Talk) 19:05, 3 August 2008 (UTC)

• It appears to be the spiniest of them all. :-) Could that be quantified?

Mathematically, no. Unless you want to formally define "spiniest"? -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

• "The Echidnahedron is the only polyhedron in our database with 180 faces."[1] Is there a deeper significance to this fact?

No. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

• Could a source be cited for the origin of the name? It seems to be the only one that is named after an animal.

According to [Mathworld], the name first appeared in the [Netlib database]. No date is given. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

• Wikipedia:Notability (numbers) is a more mathematically focused notability guideline.

That's useful, thanks. Broadly, for "number" read "polyhedron". I wonder if we should draw up a similar guideline for polygons, polyhedra and polytopes? -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

• A broad lit search for "echidnahedron" of ArticleFirst and MasterFILE Premier (both at my library) does not return any results.

The term is not widely used. Wenninger does not use it, nor can I find mention elsewhere on my bookshelf. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

• A search at http://books.google.com returns exactly one result: CRC Concise Encyclopedia of Mathematics, which I believe is a print version of Mathworld.

Says it all, really. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

--Jtir (talk) 13:43, 2 August 2008 (UTC)

I think we have pretty much confirmed that neither polyhedron nor name is notable. Concerning Gandalf61's remarks above, I would say that a Mathworld article is not sufficient credentials, the information that will be lost amounts to trivia, and there is not enough "out there" to expand the article into anything significant. However, I still think that decency demands we wait a couple of days before restoring the redirect. -- Cheers, Steelpillow (Talk) 20:16, 2 August 2008 (UTC)

P.S. Just found it in Cromwell under "complete icosahedron". Google returns about 500 hits on that, enough to keep Gandalf61 busy for a while. Looks like a longer period of grace is called for. -- Cheers, Steelpillow (Talk) 20:33, 2 August 2008 (UTC)

Good catch! "Complete icosahedron" sounds like a formal name and "echidnahedron" an informal one.

The fifty nine icosahedra does not mention "complete icosahedron".

A search at google books for "complete icosahedron" returns 30 hits, many on chemistry, and one dated 1900.

--Jtir (talk) 22:03, 2 August 2008 (UTC)

Sounds like the term "complete icosahedron" has more than one meaning:

• "A complete Icosahedron is structured with 20 equilateral triangles."[2]

--Jtir (talk) 22:18, 2 August 2008 (UTC)

"amounts to trivia" — What trivia? The element numbers could be in the info box instead of the article, but where else would a reader find them — the table in The fifty nine icosahedra does not give them. --Jtir (talk) 23:18, 2 August 2008 (UTC)

I am beginning to suspect that Cromwell's usage of "complete icosahedron" is a misunderstanding. It occurs to me that it might have a valid technical meaning in the context of configurations in projective space, where it comprises a set of 20 planes together with various joining lines and points. Any other meanings seem to be descriptive and vary with context, for example the one quoted above is probably just explaining how many faces the thing has when completed.

Anyway, looks like the clock is once again ticking on the redirect. -- Cheers, Steelpillow (Talk) 19:05, 3 August 2008 (UTC)

Found this with google. There may be more, but finding them will require access to much older bibliographies:

• "The complete icosahedron is a sixty-pointed star figure, and there are also twelve-pointed and twenty-pointed forms, and others consisting of groups of ..."

First Session of the Association. The American Mathematical Monthly, Vol. 35, No. 9 (Nov., 1928), pp. 454-456. (JSTOR)

Item 3 explicitly refers to "extending the faces of a regular icosahedron".

Does this figure predate Coxeter's work?

--Jtir (talk) 20:39, 3 August 2008 (UTC)

Nice one. Yes it does - both Bruckner and Wheeler record it, and <blushes that I didn't check before> both call it the complete icosahedron. Game set and match on the official name, then. -- Cheers, Steelpillow (Talk) 14:57, 4 August 2008 (UTC)

Thanks for confirming the standard name. Andrew Hume also considers "complete icosahedron" to be the standard name. refers to it as "the final stellation of teh icosahedron" (sic). I have created a redirect from Complete icosahedron. ISTM we could also swap the two names in the lead and perhaps rename the article. --Jtir (talk) 20:18, 4 August 2008 (UTC)

If it stays at all, yes. -- Cheers, Steelpillow (Talk) 19:42, 4 August 2008 (UTC)

I have removed the {{Notability}} tag, because notability is established by Hume having named it and Brückner having modeled it. --Jtir (talk) 22:05, 8 August 2008 (UTC)

Strictly speaking, the tag ought to have stayed there until those findings have been put in the article and not just in this discussion. -- Cheers, Steelpillow (Talk) 22:36, 8 August 2008 (UTC)

Hume in a Note, Brückner in the Refs (with associated image). AFAIK, the article does not need to say: "This article is notable because of such-and-such." I will concede that the notability is somewhere in the range of 93 and 94, say, but it is clearly greater than zero. :-) --Jtir (talk) 22:54, 8 August 2008 (UTC)

Echidnahedron as a polyhedron?

On the issue of whether the Echidnahedron is a polyhedron, I see that IF it is, topologically, it must be considered to have exactly 20 faces (from the original icosahedron), two faces per edge, 3 faces per vertex. AND looking at the stellation diagram, I see it can be considered an 2-isogonal enneagram, following the outer boundary. From this interpretation, by my count, F=20, E=90, V=60. χ=-10.

(Here's an overlay of one face on the whole figure.)

Does ANYONE accept this interpretation? (Well, this is EXACTLY how the Great stellated dodecahedron is interpreted as a regular (star) polyhedron, pentagrammic faces, triangular vertex figures.) HECK - this figure actually might deserve the name Great stellated icosahedron, except for not being regular!

Tom Ruen (talk) 22:07, 1 August 2008 (UTC)

Postscript - this simple face/vertex analysis I made above can't determine whether this is a polyhedron or a compound of polyhedra. I'd have to BUILD it to test the topology. Maybe someone else knows an easier test? Tom Ruen (talk) 23:49, 1 August 2008 (UTC)

The echidnahedron you describe is indeed a single polyhedron. Note that it has 20 faces, 90 edges and 60 vertices. There are many more examples which are neither regular nor uniform to be found among; the uniform duals, noble polyhedra (the echidnahedron being one such), many stellation forms, and so on. All this is well-known stuff and software such as Great Stella, Bulatov's stellation applet and so on will churn out the stats and images for you.

There is another interpretation of the echidnahedron, as a simple surface comprising 180 long thin triangles. This is quite evidently a single polyhedron and is equally valid. Neither interpretation is more "correct" than the other: facetting the dodecahedron leads to yours, while Coxeter's analysis in The fifty nine icosahedra dealt with the second. And there are others - for example it can be constructed as a compound of ten rather spindly trigonal trapezohedra. All this highlights the dangers of adding too much specific detail without thinking things through first, especially when the detail is fundamentally just trivia.

Sorry to be a bit of a wet blanket, but if the echidnahedron really is such a voyage of discovery for you, I think you need a bit of bedtime reading before you can make sound editing judgements. -- Cheers, Steelpillow (Talk) 12:46, 2 August 2008 (UTC)

I certainly never claimed to have the background to edit these details in the article without some confirmation of their value and accuracy. I'm just trying to express the nonconvex/intersecting star polyhedron of this echidnahedron. I think it's interesting because it is an example that has two interpretations. To me it really seems an issue of (1) abstract geometry of intersecting faces (2) real geometry of visible faces. Model builders (and apparently stellation interpretations) focus on the second. The first set is more interesting as topology while the second as physical models.

Anyway, I'd support keeping this article as a nonuniform demonstration of these two interpretations, but I accept if NO ONE IN THE WORLD but me apparently cares to show the intersecting form, it doesn't matter. Tom Ruen (talk) 22:15, 2 August 2008 (UTC)

Sorry, it re-reads harsher than I intended. If you can face picking through it again to find the sensible bits, you will find that I comment favourably on your interpretation - it is part of the well known stuff that I refer to. The many possible abstract interpretations of any given stellation form (indeed of pretty much any polyhedral form) make it pointless to investigate them unless they are particularly notable - the echidnahedron is (IMHO) showing itself not to be so. The topic of abstract structures vs. outward appearance needs a more general treatment than can be given in an article dedicated to a single polyhedron, possibly in stellation or abstract polytope. -- Cheers, Steelpillow (Talk) 19:19, 3 August 2008 (UTC)

Until decided to keep or redirect, I added a polyhedron table, made a cleaner picture. I agree it is complicated to decide from a large set of polyhedra if any are more notable than others. I could argue examples are good, but then the examples have a potentially exaggerated importance. Tom Ruen (talk) 20:02, 3 August 2008 (UTC)

possible origin of the name "echidnahedron"

Andrew Hume says he invented the name "echidnahedron":

• "... and some odd solids including the echidnahedron (my name; its actually the final stellation of teh icosahedron)."

geometry.research; "polyhedra database"; Aug 30 1995, 12:00 am.

--Jtir (talk) 21:58, 3 August 2008 (UTC)

It does look likely you've found the origin, makes sense someone who computed polyhedra coordinates would pull influence on the internet.

It looks like he is the author of a polyhedron database, and named the file for the final stellation.

• http://netlib.sandia.gov/polyhedra It's the last model in this polyhedron database.
  • :name: echidnahedron, number 141, svertices 92 ,net 180 3
  • Says: Please send errors, omissions and suggestions to research!andrew.
• Also http://www.georgehart.com/virtual-polyhedra/acknowledgments.html ... The data for most of the Johnson polyhedra originated in a database constructed by Andrew Hume [1986], and publicly available at NetLib. I modified a number of the models to correct for various minor omissions and errors.
• http://www.georgehart.com/virtual-polyhedra/netlib-info.html NetLib Polyhedra DataBase ... I have not been able to get in contact with the author about updating the files.
• And likely an ancient email: http://netlib.enseeiht.fr/liblist.html : Andrew Hume andrew@netlib.att.com and andrew@netlib.bell-labs.com (Who knows how old, or chances he'd still be at that email)

So I'd say case closed for the author, whether it is notable or not, I won't debate. Tom Ruen (talk) 22:35, 3 August 2008 (UTC)

The netlib site explicitly credits Hume for the polyhedron database here:

• lib: polyhedra (tar)

• for: angles, vertex locations, etc of geometric solids
• by: Andrew Hume
• master: netlib.bell-labs.com

--Jtir (talk) 12:31, 4 August 2008 (UTC)

This technical report by Andrew Hume is quoted and cited by Zvi Har’El in his paper on uniform polyhedra. It would be interesting to know if Hume uses the name "echidnahedron" in it, because it predates his geometry.research posting. Unfortunately, I haven't been able to find a copy online.

• Hume, A., Exact Descriptions of Regular and Semi-regular Polyhedra and Their Duals, Computing Science Technical Report No. 130, AT&T Bell Laboratories, Murray Hill, 1986.

--Jtir (talk) 15:27, 5 August 2008 (UTC)

Stub tag

Thanks to Tom's excellent work (nice star polyhedron illustration, Tom !) I would say the article is now far from stubby - it contains a similar amount of information to small triambic icosahedron, for example. So I have removed the stub tag. Gandalf61 (talk) 08:35, 4 August 2008 (UTC)

properties that are unique to this figure

What properties are unique to this figure among all the 59? It would be nice to say more than that it is the final stellation of the icosahedron. Does it have the most or least of some property, the largest or smallest? The article gives a variety of stats, but little perspective.

You should be asking, what properties are unique to this figure, never mind the 59. Basically there aren't any. It is an enneagonal icoshaedron, a final stellation, a noble polyhedron, has icosahedral symmetry, looks a bit like a spiny anteater and has so-and-so many faces, vertices and edges depending on the abstract structure you choose, etc. etc. Nothing unique in any of that. -- Cheers, Steelpillow (Talk) 21:35, 5 August 2008 (UTC)

OK, but you didn't answer the question that I asked. --Jtir (talk) 12:32, 6 August 2008 (UTC)

Why aren't any of the reference numbers 59? (I see from The fifty nine icosahedra that one sequence was chosen by the publisher, but what about the others?)

Not sure what you mean. The Crennells did number the last one in the book 59, and this is given in the article. If you mean specifically for this stellation, it's because Bruckner and Wheeler had not discovered all 58 others, and Coxeter et al. (and hence the Crennells) placed it as the eighth example due to their method for ordering their figures. -- Cheers, Steelpillow (Talk) 21:35, 5 August 2008 (UTC)

I meant specifically this version of Echidnahedron::

"It is referenced as the 17th (and final) stellation (and model W₄₂) by Wenninger and indexed 8th of 59 stellations in the book The fifty nine icosahedra. Its Du Val symbol is H."

When I read "17th", "W42", and "8th", I am left wondering why none are "59". "17th (and final)" is particularly puzzling, as it almost seems to mean 17 = 59.

W₄₂ is not used in The fifty nine icosahedra.

"their method for ordering their figures" — Where can readers find out more about their method?

--Jtir (talk) 12:32, 6 August 2008 (UTC)

Most of the points are answered in my reply above. Wenninger made models of many different kinds, only a few were icosahedra. He wrote his book many decades later. His index numbers are quite often given, which is why they are cross-referenced in this article. It is important to understand that none of these indexes has any mathematical significance - they are all just arbitrary tags. The best way to find out more is to get hold of the book. HTH -- Cheers, Steelpillow (Talk) 19:23, 6 August 2008 (UTC)

OK, and what I wrote above was intended to be comments on Echidnahedron and to identify info missing from WP. Followups at Talk:The fifty nine icosahedra. --Jtir (talk) 00:03, 7 August 2008 (UTC)

The info about where the vertices lie in relation to spheres is a nice addition. I was wondering about that. Could the radii ratios be given as decimal approximations as an aid to visualization?

--Jtir (talk) 19:24, 5 August 2008 (UTC)

Move to Complete icosahedron

It was suggested earlier that, if this article was to be kept, it should be moved to Complete icosahedron. That time seems to have arrived. Any objections? -- Cheers, Steelpillow (Talk) 14:23, 9 August 2008 (UTC)

No objection to a move/change of title, but if you do this please create a redirect from "Echidnahedron" to "Complete icosahedron", and also please go through the article and replace "echidnahedron" with "complete icosahedron" (except in reference links) so that the article's text is consistent with its new title. Gandalf61 (talk) 18:02, 9 August 2008 (UTC)

Good points. Using "complete icosahedron" throughout could sound wordy, yet "icosahedron" alone could be ambiguous. Using "complete icosahedron" in the first sentence of each paragraph and "it" or "the figure" subsequently, might suffice.

When a page is moved, redirects are created automatically.

--Jtir (talk) 19:11, 9 August 2008 (UTC)

Done. Made a few corrections/rearrangements, too. Sorry, I have broken something in the Ref/Notes mechanism. It's all too complicated for me to understand. -- Cheers, Steelpillow (Talk) 21:05, 9 August 2008 (UTC)

One of the named refs (<ref name=mw>{{MathWorld | urlname=Echidnahedron | title=Echidnahedron}}</ref>) got dropped, and there was a missing <ref/> tag. The named ref that was dropped had been sourcing this sentence:

• "... stellation of the icosahedron." (Note 4 in this version)

I put the {{fact}} on the explanation of the name echidnahedron, but don't really object to removing it, since the explanation seems fairly obvious, and I'm not sure we will ever be able to cite a source.

The lead sentence should give the definition of the term and give the alternative name in a parenthetical phrase. Here is a suggested rewrite, assuming that final stellation of the icosahedron is the definition:

• The complete icosahedron,[1] or the echidnahedron[2], is the final stellation of the icosahedron. It is "complete" or "final" in the sense that it includes all of the finite cells, into which the face planes of the regular icosahedron divide space, so it is the largest stellation of the icosahedron.
• [1] Cite Cromwell. The term is ambiguous, possibly referring to a regular icosahedron having all its faces.[exlink1]
• [2] Cite Hume.

--Jtir (talk) 22:14, 9 August 2008 (UTC)

"Final stellation of the icosachedron" first appeared in Wenninger's book. The numbered names, such as "seventh stellation of the icosahedron" were just descriptions added by his publisher, who knew nothing about polyhedra. Wenninger cannot now remember whether "final stellation" was first used by himself or thought up by the publisher, but it was always intended as a description rather than a proper name. (info from private communications, none of this is citable, so I have to be careful in what the article is allowed to say). But, due to the popularity of Wenninger's book, the descriptions have achieved status as popular names in other published sources, such as books of cut-out nets (e.g. Tarquin publications). Certainly, "Complete icosahedron" is the more formally established name: Wheeler described it as "complete", Coxeter as "Complete icosahedron", and Cromwell followed Coxeter. It is wrong to cite Cromwell, since The 59 has greater authority. The current wording is correct, butt he citations could be improved:

• Complete icosahedron [1] Cite Coxeter et al, 'The 59 (since Wheeler omitted "icosahedron").
• Final stellation of the icosahedron [2] Cite Wenninger, Polyhedron models.
• Echidnahedron [3] Cite Hume. It is named after the spiny anteater, or echidna.

-- Cheers, Steelpillow (Talk) 10:04, 10 August 2008 (UTC)

Thanks for the background info. Sounds good to me. Here is a suggested copyedit:

• The complete icosahedron[1], also called the final stellation of the icosahedron[2] or the echidnahedron[3], is the stellation of the icosahedron that includes all of the finite cells into which the face planes of the regular icosahedron divide space. It is the largest stellation of the icosahedron.

Notes as you suggest.

This combines into one sentence the alternative names and the definition. It drops any attempt to explain "complete" or "final" independently of their use in the above terms. Does a verifiable source define "complete" or "final" as terms?

I don't know what "largest" means here.

It would be a good idea to say in note 1 that "complete icosahedron" has another meaning, since anyone who does a google search can find this:

• "A complete Icosahedron is structured with 20 equilateral triangles."

'Wenninger … "final stellation"' — Interestingly, Hume uses this term in his geometry.research post.

"careful in what the article is allowed to say" — WP:V says what is allowed. :-)

--Jtir (talk) 15:06, 10 August 2008 (UTC)

I redid the citations and refs as suggested and moved the possible explanation of the name Echidnahedron to a note while phrasing it to say only what is known. I retained Cromwell as the citation for the Du Val symbol.

The lead still does not clearly define complete icosahedron and gives undue weight to the alternative names.

IMO, tetrahedron, pyramid, and lozenge are fine examples to follow.

--Jtir (talk) 16:54, 10 August 2008 (UTC)

I don't think this source[3] is NAMING an icosahedron as a complete icosahedron. It is differentiating between an icosahedron and a partial icosahedron that has some of the faces removed, like a geodesic hemisphere. Tom Ruen (talk) 17:26, 10 August 2008 (UTC)

Thanks Tom. That is my interpretation too, and you have explained it much better than I could. Anyway, an exact google search for "complete icosahedron" returns over 200 results and an exact search for "partial icosahedron" returns tens of results, some used in the context of geodesic domes. IMO, this article needs to acknowledge these facts in some way. --Jtir (talk) 17:55, 10 August 2008 (UTC)

I clarified the note by using what you said, expanding the quote, and adding another source where both complete and partial are used. How does it look?

BTW, geodesic dome doesn't actually use the term geodesic hemisphere, but I linked to it anyway.

--Jtir (talk) 18:27, 10 August 2008 (UTC)

Whatever you like, but it all seems messy, icky. Myself, I'd rather call the article descriptively Final stellation of the icosahedron, and reference Complete icosahedron and Echidnahedron as other names. Tom Ruen (talk) 20:07, 10 August 2008 (UTC)

Wondering, does ANYONE call the Great_stellated_dodecahedron a complete dodecahedron or a Stella_octangula as a complete octahedron? It ANNOYS me to have a confusing but apparently generalizeable term used if it's only used in one instance. Tom Ruen (talk) 20:12, 10 August 2008 (UTC)

Lastly, I don't like the table header As its outward form. I think it should say As a stellation or something more clearly connected to the fact it is constructed in the sellation process. (Sorry, I'm just complaining, and I don't have time this week to do much editing, so I'm being conservative with any changes.) Tom Ruen (talk) 20:15, 10 August 2008 (UTC)

"icky" — I agree. Having three names for a unique mathematical object is messy. Unfortunately, we have to go by the sources, and IIUC, Coxeter uses the term "complete icosahedron", and he has primacy.

However, the guideline for article naming, WP:MOSNAME, says that "article naming should prefer what the greatest number of English speakers would most easily recognize, with a reasonable minimum of ambiguity, while at the same time making linking to those articles easy and second nature." and that "Wikipedia determines the recognizability of a name by seeing what verifiable reliable sources in English call the subject."

Personally, I have never found the former very helpful, because it implies doing a survey of English speakers and redirects make access easy anyway. The latter is more practical, since it only implies counting usage in various sources.

"table header" — I see what you mean. Your suggestion sounds fine to me.

Could you comment on the clarity or not of the actual definition of this figure in the article?

--Jtir (talk) 20:52, 10 August 2008 (UTC)

I changed the table header, and added a table section comparing other notable forms (those that create polyhedra and compounds). I'm more comfortable showing pictures than wordy definitions, so I'm content. I now see why there's no stellated icosahedron like stellated dodecahedron. The simplest stellation extends edges while they diverge on a triangle, converge with pentagon faces. The great icosahedron has triangles faces in the same plane of the faces of the icosahedron. Tom Ruen (talk) 21:40, 10 August 2008 (UTC)

I reworked the opening, took out the unrelated stuff about nonpartial icosahedra. It seems to me that complete icosahedron' is short for complete stellation of the icosahedron. The 59 xx book lists it in the back table as complete stellation for instance. Tom Ruen (talk) 21:49, 10 August 2008 (UTC)

Thanks. That's a big improvement for the lead and the table of stellations does a nice job of providing context.

A two sentence section on the name "echidnahedron" is unlikely to expand, and the name is certainly common enough to be mentioned in the lead.[4]

I regard it as a disservice to readers to completely ignore the alternative meaning of "complete icosahedron" whose use far outnumbers the meaning in this article (as a simple google search proves). Why did you remove a sourced and documented explanation of an ambiguous term? BTW, I regard quotes in notes documenting usage of terms as a very effective way to help readers understand them. See Continental United States. If you feel the quotes are too much, it would be fine with me to say something in a note, with exlinks to sources, and with no quotes. Language is messy, and as editors we must accept that fact.

--Jtir (talk) 22:18, 10 August 2008 (UTC)

I judged this context complete icosahedron meant exclusively HERE as complete stellation of the icosahedron and other references were simply nonnotable accidents of language to differentate with nonpartial icosahedron. If this secondary usage is defendably notable then lets make this a disambiguity page and move this stellation usage to an explicit complete stellation of the icosahedron. Tom Ruen (talk) 22:42, 10 August 2008 (UTC)

OK. It sounds like you believe that a minor usage variant is beyond the scope of this article. After thinking about it, I can agree. ISTM, that icosahedron would be a better place to mention the alternative meaning. Can you suggest a place to put it in that article?

Using a dab is a good idea. Basically a reader needs to be able to find info about both meanings.

A google search for "partial polyhedron polyhedra" returns for the first result Infinite skew polyhedron. From the article, I see that partial polyhedra are a subject of mathematical interest.

--Jtir (talk) 20:13, 11 August 2008 (UTC)

other meanings of complete icosahedron

This was removed from the article, so I am putting it here to document a sourced alternative meaning of complete icosahedron.

• Sometimes complete icosahedron is used to differentiate an icosahedron having all its faces from a partial icosahedron, which has some of its faces removed, like a geodesic hemisphere:
• "A complete Icosahedron is structured with 20 equilateral triangles. By removing (truncating) the lower five triangles, … a geodesic domed structure can be built …"[5]
• "Jonesy built a complete icosahedron …"[6]

--Jtir (talk) 19:40, 11 August 2008 (UTC)

These are not proper descriptive names, they are just use of an adjective in everyday language to indicate a completed object, as a fitter selling a complete kitchen or a geek assembling a complete computer from spare parts. They are irrelevant.

The observation that The 59 uses "complete stellation" is correct. Earlier in the book, it refers to "The 'complete' stellation" - putting "complete" in quotes. Cromwell's use of "complete icosahedron" is probably a misunderstanding. This has led me to change my mind, and I now agree that "Complete stellation of the icosahedron" is more correct. Google reveals this to be far less popular than "Final stellation of the icosahedron". This last is also more popular than "echidnahedron" and is even used in at least one book title, which prompts a further change of mind and I now propose another move - to "Final stellation...". -- Cheers, Steelpillow (Talk) 20:33, 11 August 2008 (UTC)

"not proper descriptive names" — It should be obvious by now that without a "proper" definition, the word "complete" is every bit as ambiguous as that other other bugaboo, "irregular". :-) Anyway, I have conceded in the above section that mentioning any alternative meaning of "complete icosahedron" is beyond the scope of this article.

Renaming to "Final stellation of the icosahedron" is fine with me. How will that affect the wording of the definition?

"one book title" — This one?

• Jenkins, Gerald, and Magdalen Bear. The Final Stellation of the Icosahedron: An Advanced Mathematical Model to Cut Out and Glue Together. Norfolk, England: Tarquin Publications, 1985.

If no one objects, I will add it to the refs (and BTW, this book further establishes notability).

ISTM, the article could say something about how to build a model.

--Jtir (talk) 22:35, 11 August 2008 (UTC)

Stellations

The process of stellation is not very tightly defined. We cannot say that one structure for this polyhedron is a stellation while another is not. Effectively, all structures are stellations of the icosahedron. No term for the outer, visible part is in accepted use (although several arcane terms are sometimes used, but that would muddy things even worse than they are now), so I have tried to find a simple and meaningful form of words. -- Cheers, Steelpillow (Talk) 20:39, 11 August 2008 (UTC)

page layout

The page layout in this version may be a bit too logical, because it removes an image from the lead and introduces a block of white space in the middle of the article (not to mention the lead). Since the table titles match the section titles, the tables do not need to be in the corresponding section.

MOS:IMAGES has some advice on putting images in articles, and the first bit reads:

• "Start an article with a right-aligned lead image. This image is often resized to about 300px."

--Jtir (talk) 21:33, 11 August 2008 (UTC)

The problem is, we are not dealing with images but with thumping great floating tables that occupy more space than the text. IMHO this is a very bad choice, and they make mincemeat of any layout guidelines. In particluar, section breaks and inline tables flow very badly round/under them. Even if there is a visually neat layout solution, HTML and CSS2 are not really up to the task. The present layout is an attempt at compromise, but IMHO the information in the tables need a radical rethink as to what needs depicting and how best to do it. -- Cheers, Steelpillow (Talk) 08:37, 12 August 2008 (UTC)

I agree that the tables are too wide. At 800x600 they occupy 2/3 of the article width, while only 1/2 the width of Icosahedron is occupied by its infobox at the same resolution.

Why can't they be implemented as {{infobox}}es or as a template similar to {{Reg polyhedra db}}?

The other table is basically a navbox, so I reformatted it slightly and moved it to the end per WP:LAYOUT.

There is already a {{navbox}} template that resizes automatically when the browser window is resized.

--Jtir (talk) 18:58, 12 August 2008 (UTC)

By "floating tables" I meant the infoboxes - they overwhelm the page, which is not what infoboxes are meant to do. -- Cheers, Steelpillow (Talk) 12:29, 14 August 2008 (UTC)

The article is using tables (class=wikitable) instead of the {{infobox}} template.

The infobox style guide has some specific advice including:

• "Standard suggested width of 300 pixels or 25 ems (300px or 25em in CSS)."
• "Insert at the top of articles and right-align"

As for layout, one partial solution might be to put the stellation diagram below, instead of beside, the image of the complete icosahedron as a simple surface.

Both tables could be made narrower by specifying a width: {| class=wikitable align=right width=200px.

Here is a version in the sandbox with the table widths set and <br style="clear:both;"> markup removed. I don't know why the text runs up against the first box.

--Jtir (talk) 14:47, 14 August 2008 (UTC)

I think these boxes are not only too wide, but also too tall and too "in-your-face", containing so much stuff that they leave the main text with little to say. IMHO the page design needs a complete rethink, with these boxes much reduced in scope or gone altogether. -- Cheers, Steelpillow (Talk) 16:36, 14 August 2008 (UTC)

I presented this sandbox version to show that the width of the boxes could be adjusted (both are set to the total image width) and that the article layout made to conform to WP:IBX (if you look at the wikitext, you will see that the upper table has a width of 300px). The second table is too tall, but that could be fixed by removing some redundant text and moving other text to the article. The space is also being used inefficiently (e.g. the cell reading "Face type" has enough space to hold the element stats too.)

A problem in this article is that it is about two related figures, each of which seems to need its own infobox. One possibility would be to combine the two into one. Another problem is that the article text is too short to balance the infoboxes. A possibility would be to retain all the images (with brief captions), and move the facts and figures into tables in the text.

What are your suggestions for a "rethink"?

--Jtir (talk) 18:18, 14 August 2008 (UTC)

No time for me, but please rework as you like. Tom Ruen (talk) 17:05, 14 August 2008 (UTC)

Thanks for checking in. --Jtir (talk) 18:18, 14 August 2008 (UTC)

Also, I'm running out of time. I would only repeat that the two descriptions here are not the only possible ones, for example it may be seen as a compound of thirty (I think) long spindly trigonal trapezohedra. The star icosahedron is mathematically the most important of the set, but not that important. I'd suggest you put that one first and then add others as you feel the urge. -- Cheers, Steelpillow (Talk) 21:02, 14 August 2008 (UTC)

comparing the final stellation to all of the other stellations

IIUC, both of these could be said:

• "It is the largest stellation of the icosahedron." — meaning it has the largest volume of all the stellations?
• "It is the outermost stellation of the icosahedron." — meaning it encloses (contains?) all of the other stellations?

More generally, how does the final stellation relate geometrically to all of the other stellations?

Stating the obvious could be what is needed.

--Jtir (talk) 22:49, 11 August 2008 (UTC)

The "outermost" stellation does indeed comprise the outermost shell of cells/faces, which is equivalent to saying that all the other stellations may be fitted inside it while sharing the same face planes. IMHO "outermost" is sufficiently obvious that anyone who has trouble with it will have even more trouble with the expaned explanation I just gave. They can always click on a stellation link to find out more, and there is already a strong tendency in this article to repeat material that belongs elswehere.

The images in the "See also" section also do not belong there - they need either to be moved into the main body of the article or deleted. -- Cheers, Steelpillow (Talk) 08:44, 12 August 2008 (UTC)

Polyhedron of the week

See: Wikipedia:WikiProject Polyhedra‎

• I'm not sure what content can be added, but the layout now is sort of a visual jumble due to two independent interpretations of this figure, as a stellation of the icosahedron and an star polyhedron. Tom Ruen (talk) 05:20, 21 September 2009 (UTC)
• The section header Complete_icosahedron#As_a_simple_surface is strange to me. User:Steelpillow named it that from As a stellation. Tom Ruen (talk) 05:25, 21 September 2009 (UTC)
• There's an OLD source (in German) and ONLINE, source of File:Bruckner Taf XI Fig 14.JPG, that deserves some explaining anyone can read it! Tom Ruen (talk) 06:01, 21 September 2009 (UTC)
  • Brückner, Max (1900). Vielecke und Vielflache: Theorie und Geschichte. Leipzig: B.G. Treubner. ISBN 978-1418165901. (in German)

WorldCat English: Polygons and Polyhedra: Theory and History. Photographs of models: Tafel VIII (Plate VIII), etc. High res. scans.

GA Review

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

Hello, I will be the reviewer for this article. I may not be a mathematician, but I feel that this article could use more content. The fact that the article has two sections is very scary. They discuss the properties of the complete icosahedron, but I don't see info on why it's important in math. Is it merely a type of solid, or does it possess special properties that are notable in the mathematical community? Are there any practical applications in real life?

• I have added some more information to the article. The unique property of the complete icosahedron is that it is the final stage in the stellations of the icosahedron, it includes all of the regions in the icosahedron's stellation diagram, and as such is arguably the most complex object that can be produced from the regular Platonic solids. As far as I am aware, it has no practical applications in real life. Do you have any more suggestions for additional content ? Gandalf61 (talk) 11:09, 9 October 2009 (UTC)
  • The additional content is certainly helpful. Could you briefly explain the stellation diagram? This would definitely be helpful to average readers who aren't familiar with the topic. --Edge3 (talk) 21:10, 9 October 2009 (UTC)

• Added a link to stellation diagram. Gandalf61 (talk) 22:08, 9 October 2009 (UTC)

• Also, I think that you should explain the following: "The Du Val symbol of the complete icosahedron is H."--Edge3 (talk) 21:10, 9 October 2009 (UTC)

• Added a brief explanation. Gandalf61 (talk) 22:08, 9 October 2009 (UTC)

Also, the lead is supposed to be only a summary of the body of the article. See WP:LEAD. I recommend that you move the detailed info to body paragraphs and expand them.--Edge3 (talk) 02:11, 9 October 2009 (UTC)

• I have changed the lead and created a new "Background" section for some material that was previously in the lead. Gandalf61 (talk) 11:09, 9 October 2009 (UTC)

• Provide basic info on the golden ratio, and point out that it's represented by phi. This will cause less confusion in the "As a three-dimensional solid" section--Edge3 (talk) 22:54, 9 October 2009 (UTC)

• I have added a link to the golden ratio article. Gandalf61 (talk) 07:35, 10 October 2009 (UTC)

• "It is sometimes called the echidnahedron[5] after the echidna, or spiny anteater, a small mammal that is covered with coarse hair and spines." - Not supported by source.--Edge3 (talk) 03:25, 10 October 2009 (UTC)

• Okay, I have taken out "after" and put the explanation of echidna in brackets. Readers may draw their own conclusions. Gandalf61 (talk) 07:35, 10 October 2009 (UTC)
  • Do you have a source to back up the claim that many, not just one, mathematicians call it the echidnahedron?--Edge3 (talk) 21:07, 10 October 2009 (UTC)

• Not many, but more than one - the term is used in references 6 and 7. But I have changed "It is sometimes called" to "It has been called". Gandalf61 (talk) 21:34, 10 October 2009 (UTC)
• The echidnahedron naming is used with the Mathematica community and MathWorld, sourced back to a polyhedron database library in the 1990's. The reference is now moved to the history section. Tom Ruen (talk) 07:58, 11 October 2009 (UTC)

• The Coxeter source seems useless in the first sentence. Perhaps it would be more relevant in the first paragraph of the Background section. --Edge3 (talk) 04:11, 10 October 2009 (UTC)

• The Coxeter source is important because it shows that the article,s title, "complete icosahedron", is indeed used in the literature to refer to this object, and is not a neologism or another term for the great icosahedron etc. This needs to be established in the lead, where the term if first used. I think the reference should stay where it is. Gandalf61 (talk) 07:35, 10 October 2009 (UTC)

• Ok--Edge3 (talk) 21:07, 10 October 2009 (UTC)

• I would also like to see at least one source in the begging of the "As a star icosahedron" section. (WP:SCG) --Edge3 (talk) 21:13, 10 October 2009 (UTC)

• I have added a source and have rewritten the paragraph so that the calculation of the numbers of sides, vertices and edges is clearer. Gandalf61 (talk) 21:57, 10 October 2009 (UTC)

• Good job! Does 9/4 refer to Schläfli symbol? If so, please provide a link. --Edge3 (talk) 22:27, 10 October 2009 (UTC)

• • 9/4 is similar to Schläfli symbol, {9/4}, but the second implies a regular star polygon. But it has the same "winding" rule - 9 pointed star, connecting every 4th vertex, so it wraps around the origin 4 times to complete. Tom Ruen (talk) 02:37, 11 October 2009 (UTC)

• File:First compound stellation of icosahedron.png and File:Zeroth stellation of icosahedron.png both have very ambiguous licences. Would you happen to know if they're free or not?--Edge3 (talk) 22:38, 10 October 2009 (UTC)

• I just posted a message on the talk page of the uploader, Tomruen. --Edge3 (talk) 02:01, 11 October 2009 (UTC)

I emailed the Vladimir Bulatov, offered some friendlier licensing options. I emailed him before when I first uploaded the images. Tom Ruen (talk) 02:35, 11 October 2009 (UTC)

Ok. The other pictures in the template are still free, right?--Edge3 (talk) 02:50, 11 October 2009 (UTC)

I really HATED the sectional flow as it was, so I reworked it significantly, hopefully better. It would be nice to expand the history more, but at least I added two short statements about Brückner and Wheeler. Overall it is sort of confusing, really three things going on (1) Stellation generation (2) Visible surface polyhedron interpretatio (3) Star polyhedron interpretation. All three deserve attention. Tom Ruen (talk) 04:01, 11 October 2009 (UTC)

I like what you've done. I was actually planning to recommend name changes for the sections, but you pretty much took care of it. Here are a few more recommendations:

• Change the heading of the first table/infobox from "As a simple surface" to "Complete icosahedron".
• Try to get a summary of the History section in the lead per WP:LEAD. --Edge3 (talk) 04:11, 11 October 2009 (UTC)
• Move File:Icosahedron stellation diagram center.png to the "As a simple surface" section
• Move File:Bruckner Taf XI Fig 14.JPG to the top of the History section--Edge3 (talk) 04:18, 11 October 2009 (UTC)

Okay, I'm done, not satisfied, but all my brain can handle, glad if anyone else wants to rework differently. I reduced a unified the stat table to the bare minimum, and moved more pictures to each sections. I really felt it needed 3 sections, the stellation construction, and the two distict interpretations. I expanded the history section, moved it to the end, but unsure what's a good placement. Tom Ruen (talk) 06:10, 11 October 2009 (UTC)

Do you have a source for the Kepler info in the history section?--Edge3 (talk) 14:56, 11 October 2009 (UTC)

• Done. Gandalf61 (talk) 16:58, 11 October 2009 (UTC)

I've combined all three sections into an Interpretations section. Also, I think that the stellation information in the lead should be shortened, and the rest of the info could be moved to the "As a stellation" section. Remember that the lead should primarily be a summary of what's in the body. --Edge3 (talk) 15:18, 11 October 2009 (UTC)

• Done. Gandalf61 (talk) 16:58, 11 October 2009 (UTC)
  • Could you please add a summary of the History section to the lead as well?--Edge3 (talk) 17:13, 11 October 2009 (UTC)

• Done. Gandalf61 (talk) 08:42, 12 October 2009 (UTC)

Final review

GA review (see here for criteria)

---

This article now is worthy of GA status, but there is always room for improvement.

1. It is reasonably well written.

   a (prose): b (MoS):

2. It is factually accurate and verifiable.

   a (references): b (citations to reliable sources): c (OR):

   Most of the info provided qualifies as common knowledge (among mathematicians) and therefore don't need a lot of sources.

3. It is broad in its coverage.

   a (major aspects): b (focused):

   The History section could always be expanded into full paragraphs, but that's not necessary for GA purposes.

4. It follows the neutral point of view policy.

   Fair representation without bias:

5. It is stable.

   No edit wars, etc.:

6. It is illustrated by images, where possible and appropriate.

   a (images are tagged and non-free images have fair use rationales): b (appropriate use with suitable captions):

   All images have good captions. The two images mentioned above have licensing issues, but I'm not going to let that delay the GA process.

7. Overall:

   Pass/Fail:

   Good job!

Proposed move

I believe that this page has the wrong name.

Firstly, Wenninger (Polyhedron models) calls this figure the Final stellation of the icosahedron. Coxeter et al (The fifty nine icosahedra) refer to it as the "complete" stellation (their quotes). Wheeler (Certain forms of the icosahedron ... ) merely notes it as complete. Unfortunately Brückner's obtuse prose (Vielecke und vielflache) defeats me. Only Cromwell says it is called the complete icosahedron, but he offers no antecedent for this observation. Cromwell is not always uncontentious in these little remarks (for example he regards the quasiregular duals as de facto quasiregular, a position which is not held by any other authority).

Meanwhile, in projective geometry the complete icosahedron is something else entirely - a (not particularly notable) configuration of 20 planes and all their 3-fold (or higher) points of intersection (and optionally, depending on your understanding of a configuration, the various lines in space along which two planes meet).

Therefore I believe that Cromwell is mistaken, and this page should be moved to either Complete stellation of the icosahedron or Final stellation of the icosahedron. Since the second of these already exists, I propose that we move this page there, over the existing redirect to this article. -- Cheers, Steelpillow (Talk) 21:46, 7 December 2009 (UTC)

Article names should be concise, recogniseable and easy to find. I think complete icosahedron is a better name than Final stellation of the icosahedron on all three counts. Gandalf61 (talk) 22:49, 7 December 2009 (UTC)

A concise title is great - unless it refers to something else entirely. The only reference for the present usage is Cromwell, and IMHO that is dubious. The phrase "complete icosahedron" has various meanings (see Talk:Complete icosahedron/archive1) - that makes Final stellation of the icosahedron more recognisable. A Search on "Final stellation of the icosahedron" just returned 2,500 hits, while "Complete icosahedron", with all its various meanings, got a mere 1,210. That makes "Final stellation of the icosahedron" easier to find, too. I make that "Final stellation of the icosahedron" - 3, "complete icosahedron" - 0. -- Cheers, Steelpillow (Talk) 20:48, 9 December 2009 (UTC)

BTW, Talk:Complete icosahedron/archive1 contains some other interesting observations, including the use of ""Final stellation of the icosahedron" in the title of a book. -- Cheers, Steelpillow (Talk) 20:55, 9 December 2009 (UTC)

For the record, I still disagree with your proposed move, but I see you are going ahead with it anyway. Gandalf61 (talk) 17:57, 12 December 2009 (UTC)

You still have time to build your case against the move, and answer the points made. I was careful to use the procedure for a move which might be contested. (updated) -- Cheers, Steelpillow (Talk) 17:44, 14 December 2009 (UTC)

For background on this article's names: [7]

• Oct 22, 2005 Tomruen (talk | contribs) (create stub article) *** Created as Seventeen stellation of the icosahedron from count in Wenninger
• Jan 12, 2006 Salix alba (moved Seventeenth stellation of icosahedron to Final stellation of the icosahedron) *** This is actual name given by Wenninger
• Jul 10, 2008 Tomruen (moved Final stellation of the icosahedron to Echidnahedron: proper name) *** Name used on Mathworld, later determined to be from an author of a polyhedron computer database
• Aug 9, 2008 Steelpillow (moved Echidnahedron to Complete icosahedron over redirect: As agreed per discussion)

Myself, I have no preference, shorter is nicer, but it can be kept as a redirect anyway. Tom Ruen (talk) 19:58, 12 December 2009 (UTC)

Requested move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was page moved. Anthony Appleyard (talk) 21:42, 20 December 2009 (UTC)

---

• Complete icosahedron → Final stellation of the icosahedron — Move over redirect: the existing title is less commonly used, ambiguous, and may even be incorrect. For more, see the recent and archived discussions. ---- Cheers, Steelpillow (Talk) 15:19, 12 December 2009 (UTC)
• Casting vote Anthony Appleyard (talk) 21:42, 20 December 2009 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

I've turned Complete icosahedron into a disambiguation page

Complete icosahedron is now a disambiguation page which is based largely on Steelpillow's comments here. A number of articles still link to it but I might see which ones I can disambiguate myself. —Pengo 22:39, 6 September 2010 (UTC)

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