Wikipedia:Articles for deletion/List of Taylor polyhedra


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was delete. Mr. Taylor, you should not write about your own research in Wikipedia. If it is of any significance, others will do that for you.  Sandstein  20:21, 19 June 2016 (UTC)

List of Taylor polyhedra

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No evidence that this term is used by anyone other than the author of those self-published references, nor if these polyhedra are named and discussed by anybody else. Given the interpretation of {4/2} used here as a compound of two digons, going directly against the work of Grünbaum and others who have published on similar degenerate uniform polyhedra, I doubt there is any. Double sharp (talk) 08:12, 10 June 2016 (UTC)

My name is Patrick Taylor; some years ago I discovered that it is possible to create a series of polyhedra based on the symmetry {4,4/2} that produces a set of forms directly analogous to the star polyhedra based on {5,5/2}; I have published extensively on this and nowhere have I ever used the term 'Taylor Polyhedra'; What happened was that someone picked up my work, liked it and without my knowledge created a Wikipedia page entitled 'List of the Taylor Polyhedra';

I felt honoured at being so recognized; Originally the page included many other forms from my published work not included in the official 'Uniform Polyhedra', but later I edited it down to cover just those that involved the {4/2} symmetry, which I had discovered, and which I felt truly deserved their own place in the limelight;

I used the term {4/2} for the cross polygon symmetry because it works and felt natural and it truncates to a double square in exactly the same way the star polygon {5/2} truncates to a double pentagon; I thus believe Grunbaum's reading of this is unhelpful; My own work builds the case from first principles for the numbering of polygons and their truncations in the way I have found most useful;

What really concerns me though is the way someone who thinks they know better can come along and redirect people off what I consider my page, containing my discoveries, sending them to their page, which itself does not actually contain any of the forms I describe; They have effectively wiped off of Wikipedia any reference to my discoveries which stand separately from the acknowledged polyhedra;

This is not the way things move forward and does not encourage new discoveries as I think Wikipedia should; I find it very difficult and time consuming to deal with the strange conventions of Wikipedia, so if you let this page go off the radar now, it will be your loss: I will still have this odd corner of knowledge to myself, as will anyone who cares to buy my printed publications

Polystar (talk) 19:22, 10 June 2016 (UTC)
 * Note: This debate has been included in the list of Mathematics-related deletion discussions. NewYorkActuary (talk) 03:58, 11 June 2016 (UTC)


 * Delete . The sourcing simply doesn't meet our standards for inclusion and from the above discussion is unlikely to be improvable any time soon. Also because the existing red sea here is manifestly not useful for anyone hoping to learn something useful about this subject, but (for the same sourcing reasons) is again unlikely to be improvable. —David Eppstein (talk) 04:59, 11 June 2016 (UTC)

I would be happy to engage in further discussion, but find some of your terms unintelligible: what is sourcing? what are these sourcing standards? what is improvable? and where does the red sea come into the discussion? If improving the presentation to enable more to be learnt is a problem, then I do have ample illustrations of all the polyhedra concerned (I had to draw them for my publications), but I am a little daunted at how to upload them: at present my time is better spent moving my geometric theory onwards to deal with the skew polyhedra in four dimensions, rather than struggling with Wikipedia's formatting problems: You do not have a page on that new subject either so if I make one in due course, will that get redirected to a page that does not include any of that material at all? Polystar (talk) 08:25, 11 June 2016 (UTC)

Some further thoughts for your consideration: the reason these polyhedra are not named or discussed by anyone else is that I am the one that has named them and published them; some of them do appear in Holden's book ('Shapes and Symmetry' if I recall correctly) as 'nolids' however when you fill in the gaps to create the whole {4,4/2} family of forms, most actually do have three dimensional volume; what seems to be missing here is any recognition that I have created original work, adding something that has not been published before and which parallels exactly another symmetry family of accepted polyhedra {5,5/2}; I find the denial of the existence of these forms by those who would delete my page almost medieval, trying to refer interested parties back to another page where they do not exist has a touch of the flat earth about it  Polystar (talk) 06:59, 12 June 2016 (UTC)

Presumably the same will hold for my work on the tilings published in 'Incomplete Tilings' (1998): here I include the {6,6/2} symmetry family where {6/2} is a 'Star of David', probably not as Grunbaum would have it; These could easily be called the Taylor Tilings, but I have not been so presumptuous;  They again include a full range of truncations completely analogous to the {5,5/2} star polyhedra family, the book as a whole including various other tilings that can be derived by considering different Schwarz triangles; Would it be possible to put forward a Wikipedia page covering these, or would that too get deleted because the material has not been described before by someone else? Original research here seems to be suffering discouragement Polystar (talk) 14:59, 12 June 2016 (UTC) So the question now seems to be whether anyone else has used my work or referred to it so as to be a 'secondary source': the only such person I know of is Douglas Boffey who started this all off by liking what I had published enough to set up the page in the first place, a not inconsiderable piece of work in itself; This is a very fringe subject and the ideas not something likely to be in common circulation, so how does a new piece of geometry get established other than by being published and then hopefully picked up and discussed further?: I have done the publication bit and this forum seems to be the only place where any discussion is taking place, but that discussion is all about whether my work should be deleted or not depending on your guidelines, rather than about whether it is correct or significant, which is the discussion needed to get past your guidelines: catch 22 I think is the term used;  I find this all rather discouraging and would have hoped that those denigrating my work, would have at least read it as published in full rather than relying on what appears on the page which is but a summary and not illustrated as yet Polystar (talk) 07:23, 13 June 2016 (UTC)
 * Delete - Article does not pass WP:GNG. you can go to WP:GNG to read the guideline on sourcing. You need secondary, reliable sources in addition to your primary sources. DeVerm (talk) 20:51, 12 June 2016 (UTC)
 * please do understand that we have nothing against you nor your work. Personally, being a retired electronics & IT engineer, I am charmed by anything related to math, science and engineering. The thing is that Wikipedia records history, it does not participate in creating history other than it's own. You have your sights aimed at the wrong podium for your work. This is the same for everybody, not just you or a group. We are not denigrating your work nor would we tolerate anybody doing so on Wikipedia; in fact, I look forward to your work meeting the guidelines and having a good article on Wikipedia that can stand any test like this, because it means that the scientific community has recognized and validated your work! Don't give up. DeVerm (talk) 14:20, 13 June 2016 (UTC)


 * Delete (duh).
 * this is Wikipedia, an encyclopedia, not a collection scientific newspapers. It should not publish original research.
 * While there are sometimes reasons to "get past the guidelines", those are rare (and "but my work is important!" is never a good reason). If you disagree with the guidelines (WP:OR or WP:GNG) themselves, you could try to get them changed at WP:VPP but your chances are extremely thin considering that (unlike other obscure Wikipedia guidelines) those are core principles.
 * When people say your work is "not notable", it does not imply that it is worthless or wrong. If Wikipedia existed in 1543, an article about Copernicus' book would almost surely be deleted, and (at least until 1620 or so) heliocentrism would be labelled as a fringe theory if mentioned at all. It may be that your work will be recognized later on, but Wikipedia is not the place to promote your ideas nor to assess their worth. Tigraan Click here to contact me 12:13, 13 June 2016 (UTC)

Going back to the original complaint at the top of this discussion, which I reproduce here:

"No evidence that this term is used by anyone other than the author of those self-published references, nor if these polyhedra are named and discussed by anybody else. Given the interpretation of {4/2} used here as a compound of two digons, going directly against the work of Grünbaum and others who have published on similar degenerate uniform polyhedra, I doubt there is any."

I did not originate the term 'Taylor Polyhedra', someone other than me, i.e. Douglas Boffey did that as your records will show; These polyhedra are discussed elsewhere as some are shown in Holden's book 'Shapes and Symmetry' as 'nolids', and most have been published in a paper I presented in Delft at a conference some years ago, which was independently reviewed and published in the proceedings (I cannot lay my hands on details just now but have a copy back home); The interpretation of {4/2} I use is entirely in accordance with the Schlafli notation and your own Wikipedia page on Schlafli symbols shows {6/2}, {8/2} and {9/3} exactly as I would interpret them, a pair of out of phase triangles, a pair of out of phase squares and three out of phase triangles respectively, i.e. 'directly against the work of Grunbaum' who would have these numbers representing a pair of coincident triangles, a pair of coincident squares and three coincident triangles respectively; The question that arises here is what symbol does Grunbaum actually allocate to the Star of David or hexagram which I call {6/2} and what does he get when he truncates it? I get a double coincident hexagon as the result, which Grunbaum would I think call {12/2}?

The important thing here is that what I have done in whatever notation we choose, leads to an interesting set of symmetries not before acknowledged or explored; Both {4,4/2} and {6,6/2} yield full sets of truncations completely analogous to the generally accepted {5,5/2} family of star polyhedra; Surely this knowledge should not be consigned to the trash bin without some consideration of its merits and certainly not in a way that redirects the enquirer to a page that does not even acknowledge that knowledge's existence and which slavishly follows a particular interpretation of polygon notation, which I think is mistaken as it does not include all polygons Polystar (talk) 08:02, 14 June 2016 (UTC)
 * I suspect Grünbaum would say that your {6/2} is not actually a polygon at all, as its edges do not form a single closed circuit. He would call it 2{3}, as it is a compound of two triangles. The difference between {12/2} and t(2{3}), then, is that the first is a dodecagon (it has 12 edges, going ABCDEFGHIJKL and then ending up back at A, it being a complete accident of realisation that A and G coincide – as an abstract polytope they are distinct vertices, and in fact this is no different from the regular non-degenerate dodecagon {12}), while the second is two coinciding hexagons (each of which has 6 edges; they may coincide completely, but their vertex circuits don't contain any common elements, being ABCDEFA and GHIJKLG. Again, it does not matter that A coincides with G. If you like, you can informally think of this shape as the limit of two hexagons as they get closer and closer. By informally thinking of continuity, as I shove the hexagons into and past each other, there is no reason why the number of vertices and edges I have should suddenly halve when they coincide completely for a brief moment).
 * Please understand that I have nothing against your work in particular. I might not agree with your notation, or indeed some of your interpretations of what is going on with these polyhedra, but I am not advocating its deletion from Wikipedia for these reasons. I am doing that because it is your original research, which, while it certainly would have a place in a journal, is not yet notable enough for Wikipedia by our policies. I originally redirected it because I wanted to save its history at least on Wikipedia (if you click "view history" on a page you can get older versions), but since you reverted it it appears to have to be off Wikipedia for the time being. Double sharp (talk) 11:30, 14 June 2016 (UTC)

I appreciate the difference between Grunbaum's {12/2} and t2{3}, but it does highlight the fact that Grunbaum does not have a notation for the double polygons obtained by truncating compounds with even denominators, other than calling them t2{3} (or t2{2} in the case of the truncation of the cross polygon which I call {4/2}); He is prevented from calling these 2{6} or 2{4} respectively because these notations belong in his book to out of phase pairs of polygons rather than coincident ones;  Whilst there may be good topological, set theory or other reasons for only dealing with complete continuous circuits of vertices in his work, we are dealing here with polyhedra, some of which we have to accept as compound and which accordingly have compound truncations, requiring compound truncated polygons to make them up;

Interestingly it is the even denominator rather than the 'being compound' that causes the problem, for {9/3}, or 3{3} in Grunbaum's notation, truncates to {18/3}, or 3{6} for Grunbaum: all neat and tidy; What I am saying then is that if we are to be able to describe the various compound polyhedra and tilings satisfactorily, we need to adopt a notation that allows for the truncations of {4/2}, {6/2} and its inverse {6/4} to be described in a meaningful way without ambiguity: my solution sticks with the numbers just given for the original polygons in accordance with Schlafli and then introduces the double square, double hexagon and double hexagram respectively for the truncations which are two coincident squares, hexagons or hexagrams;  These truncations sit well within the series that includes double triangle and double pentagon as the truncations of {3/2} and {5/2}, but which Grunbaum describes as {6/2} and {10/2}, numbers which Schlafli gives a definite different meaning to;

The question seems to boil down to who is right: Schlafli or Grunbaum? and if it is the latter then the Wikipedia page on star polygons needs editing accordingly as the notation there is all Schlafli's

Polystar (talk) 10:54, 15 June 2016 (UTC)
 * Delete as per above arguments - fails WP:GNG, not likely to be improved. Gandalf61 (talk) 14:57, 15 June 2016 (UTC)
 * Delete. No evidence of notability. No sign of significant coverage in reliable sources.  B E C K Y S A Y L E S  09:48, 17 June 2016 (UTC)
 * Delete as it's only his own sources and my searches have found nothing better, nothing for independent notability. SwisterTwister   talk  06:38, 19 June 2016 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.