User talk:SteveWoolf

Letter to Peter McMullen
Dear Peter Your reply much appreciated, and I have shared it with the other APists on Wikipedia, hope that's ok. 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.

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:

(1) The polytope (poset) is a lattice, i.e. has meets and joins

(2) It is atomistic and coatomistic - i.e. every k-face is a join of vertices and a meet of facets.

I have also seen it stated that

(3) Polytopes have distributive lattices (Meet~Join). I have yet to mull over the significance of this.

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).

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 useful.

I am hoping that the outcome of this would a nice general theorem to the effect:

Every abstract polytope satisfying the above conditions is (combinatorially) isomorphic to a combinatorial equivalence class of "traditional" polytopes.

Of course, both the "above conditions" and "traditional" will first need rigorous definition.

Maybe also these conditions are also equivalent to faithful realizabilty...? 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.

Regards Steve

PS:

I CC'd this to Egon Shulte also, I hope that is appropriate. Should you happen to browse Wikipedia'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.

--- On Fri, 12/12/08, Peter McMullen wrote:

From: Peter McMullen Subject: Re: "Classical" vs "Traditional" Polytopes Cc: "Egon Schulte"

Dear Steve,

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 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.

I hope that this clarifies my viewpoint. I imagine that Egon Schulte will have his opinions, but I would be surprised if they differ very much from mine.

With best regards -  Peter.

Your recent edits
Hi there. In case you didn't know, when you add content to talk pages and Wikipedia pages that have open discussion, you should sign your posts by typing four tildes ( &#126;&#126;&#126;&#126; ) at the end of your comment. If you can't type the tilde character, you should click on the signature button 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! --SineBot (talk) 05:21, 25 December 2008 (UTC)

Barnstar
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! SteveWoolf (talk) 22:15, 16 June 2010 (UTC)

Sincere apology
Steve, I am sorry that my recent efforts with Abstract polytopes 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 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. &mdash; Cheers, Steelpillow (Talk) 13:25, 6 June 2010 (UTC)

Expired Login
Hi bluerasberry sorry an oversight

Abstract polytope barnstar

 * 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 talent to the field. SteveWoolf (talk) 22:28, 16 June 2010 (UTC)

Hasse diagrams, vertex sets and editing
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. &mdash; Cheers, Steelpillow (Talk) 16:57, 19 June 2010 (UTC)


 * I see that you are not happy with Mike40033's removal of your disruptive editing 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.


 * 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 disruptive editing and the Hasse diagram is disrespectful, and any detailed reply would serve no useful purpose.


 * I remain genuinely puzzled that at times you seem to acknowledge that "in AP theory, it is not required that faces are defined as vertex sets" while at other times you seem to insist that "If we formalise completely, then our faces are sets of vertices". 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 abc notation, using say F instead. Does ARP describe j-faces as vertex sets and/or use the abc notation, and if not then what is your reference point?


 * &mdash; Cheers, Steelpillow (Talk) 19:39, 20 June 2010 (UTC)

Abstract polytopes
You have previously contributed to the Abstract polytope article. If you feel able, please contribute to the discussion on Notation, where I am hoping to resolve a long-standing dispute. Many thanks in anticipation.

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. &mdash; Cheers, Steelpillow (Talk) 14:50, 17 July 2010 (UTC)

File:Bicube.PNG missing description details
Dear uploader: The media file you uploaded as: 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.
 * File:Bicube.PNG

If you have any questions, please see Help:Image page. Thank you. Message delivered by Theo's Little Bot (opt-out) 15:50, 14 June 2013 (UTC)

File:Bicube.PNG listed for deletion
A file that you uploaded or altered, File:Bicube.PNG, has been listed at Files for deletion. Please see the 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. Sfan00 IMG (talk) 09:19, 3 August 2013 (UTC)

Notification of automated file description generation
Your upload of File:Amorphic Polyhedron.PNG 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.

This notification is placed on your talk page because a bot has identified you either as the uploader of the file, or as a contributor to its metadata. It would be appreciated if you could carefully review the information the bot added. To opt out of these notifications, please follow the instructions here. Thanks! Message delivered by Theo's Little Bot (opt-out) 11:49, 24 December 2013 (UTC)


 * Another one of your uploads, File:Apeirogonal Apeirohedron.PNG, has also had some information automatically added. If you get a moment, please review the bot's contributions there as well. Thanks! Message delivered by Theo's Little Bot (opt-out) 12:06, 31 December 2013 (UTC)

ArbCom elections are now open!
Hi, You appear to be eligible to vote in the current Arbitration Committee election. The Arbitration Committee is the panel of editors responsible for conducting the Wikipedia arbitration process. 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 site bans, topic bans, editing restrictions, and other measures needed to maintain our editing environment. The arbitration policy describes the Committee's roles and responsibilities in greater detail. If you wish to participate, you are welcome to review the candidates' statements and submit your choices on the voting page. For the Election committee, MediaWiki message delivery (talk) 13:55, 24 November 2015 (UTC)