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Really appreciate that Guy - I hope I will have time to make AP a truly magnificent article by properly integrating all the material and expanding it, but in ways that will please everybody. My dream is that the article will make AP theory accessible to a much wider audience, and thereby bring more
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In my recent usage, I have reserved "classical" for the regular polytopes of (for example) Coxeter's book "Regular
Polytopes". I suppose that these are also the "traditional" regular polytopes. More generally, I have been calling a realization of an abstract polytope a "geometric" polytope. Thus
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I realise that trying to characterise "traditional" polytopes in abstract terms is difficult without a precise definition of "traditional". Nevertheless, out of the several possible concepts of traditional, I suspect one may be better - more elegant, more easily characterised in AP terms, and more
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I too am a reasonably experienced and by and large successful wikipedia editor. I too have sought diligently and under duress from my family to improve this article. The reality is that we are two strong and determined characters in a genuine dispute about what is best. However your tone on
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Steve, have no fear, I will not revert wholesale however much I might want to - that was a heartfelt cry, not a threat. I'll answer some of your other points when I have taken a break - probably here because much of this is more about our differences than about the article itself. — Cheers,
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have upset you so much. I am indeed competent in much of the more traditional polytope theory and its relation to abstract polytopes, without being competent in the finer points of set theory. The necessary joining of minds was taking time and energy and, being human, I was evidently not as
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Thanks - I only just saw your message! But your kind words make me feel all my efforts are worthwhile. PS There is lots of good material in the rather chaotic AP Discussion page - it needs references which I can't find, and tidy up - which I can do. Hope to see you around again soon!
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or contribution to its description is noted, and thanks (even if belatedly) for your contribution. In order to help make better use of the media, an attempt has been made by an automated process to identify and add certain information to the media's description page.
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the main contrast is between "abstract" and "geometric" polytopes. Of course, the latter (regular, chiral and even more general objects such as incidence complexes) are often investigated in their own right, particularly in a dimension-by-dimension classification.
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While I am sure (1) and (2) are necessary, I am not clear whether these conditions (with or without (3)) are sufficient, or independent given your other 4 standard AP axioms (bounded, graded, strongly connected, and having the "diamond" property).
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Steve, I have asked the above of several current and former editors of the article. Much of your work has been valuable, and I would also appreciate your POV here. For example your memory of the history may be different from mine. — Cheers,
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located above the edit window. This will automatically insert a signature with your name and the time you posted the comment. This information is useful because other editors will be able to tell who said what, and when. Thank you!
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considerate as I should have been. So I can understand your need to pull away for now, but overall the article has benefitted greatly from your contributions and I do hope that in due course you will feel able to return. — Cheers,
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I am currently trying to define, in strictly formal AP terms, a subclass of "nice" abstract polytopes that correspond more closely to the traditional (pre-abstract) concept of polytope, i.e. that would not include eg the digon.
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is missing a description and/or other details on its image description page. If possible, please add this information. This will help other editors make better use of the image, and it will be more informative to readers.
582:. It has the authority to enact binding solutions for disputes between editors, primarily related to serious behavioural issues that the community has been unable to resolve. This includes the ability to impose
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Should you happen to browse
Knowledge's AP article and talk page, my humour is occasionally a little irreverent, but I try never to write anything that might cause real offense, and no disrespect is intended.
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to see why it has been listed (you may have to search for the title of the image to find its entry). Feel free to add your opinion on the matter below the nomination. Thank you.
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It seems that such AP's, i.e. those that are combinatorially equivalent to some (combinatorial equivalence) class of traditional polytopes would have at least these properties:
357:". We have agreed that we should be guided by M&S, and especially by ARP. The papers by M&S that I have to hand make no mention of vertex sets and also avoid the
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I hope that this clarifies my viewpoint. I imagine that Egon
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remarks. Since they are off topic and directed entirely at me, I think our usertalk pages are a better home for them. At any rate, I respond briefly here.
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Every abstract polytope satisfying the above conditions is (combinatorially) isomorphic to a combinatorial equivalence class of "traditional" polytopes.
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As it seems probable that you have already covered this ground, I would be most interested in your comments on the above, if you have time.
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disruptive editing and the Hasse diagram is disrespectful, and any detailed reply would serve no useful purpose.
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Your reply much appreciated, and I have shared it with the other APists on
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Of course, both the "above conditions" and "traditional" will first need rigorous definition.
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From: Peter McMullen
Subject: Re: "Classical" vs "Traditional" Polytopes Cc: "Egon Schulte"
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I am hoping that the outcome of this would a nice general theorem to the effect:
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Maybe also these conditions are also equivalent to faithful realizabilty...?
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article. If you feel able, please contribute to the discussion on
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If we formalise completely, then our faces are sets of vertices
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I CC'd this to Egon Shulte also, I hope that is appropriate.
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Hi there. In case you didn't know, when you add content to
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notation, and if not then what is your reference point?
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Notification of automated file description generation
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164:The Graphic Designer's Barnstar
602:. For the Election committee,
572:Arbitration Committee election
563:ArbCom elections are now open!
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105:With best regards - Peter.
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