Talk:Hypercube

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[edit] redirect to tesseract

I changed the redirect from measure polytope to Tesseract. I agree a hypercube can imply HIGHER polytopes than a tesseract, but 99% of the time I expect people MEAN a 4-polytope, so I judge it better to link to tesseract specifically and let readers go to the more general (family) secondly from there. Tom Ruen 06:21, 14 October 2006 (UTC)

Since my redirect was reversed, I removed the redirect and put two links in here.

I still disagree - I NEVER mean "n-dimensional hypercubes" and say hypercube since that is ambiguous what I mean. I'd say n-cube or n-hypercube or n-measure polytope. If there's no dimension offer I assert 4 is implied. Tom Ruen 09:47, 12 November 2006 (UTC)

I disagree. I ALWAYS mean the general case when I say "hypercube", and would specify 4-dimensional if that's what I mean. I don't think 4d is the default, and I think hypercube should be the preferred name for what is now measure polytope. I see tesseract as a special case, that should be prominently linked from the hypercube page but not redirected from it. And according to WP:D disambiguation pages (such as the current state of this page) are for when there are several links to disambiguate, but here there are only two. —David Eppstein 18:18, 15 November 2006 (UTC)

Later: I made this a little more texty and added a link to hypercube graph. So now it looks a little more plausible as a dab page. I'd still prefer this to be the main name for measure polytope, though, and am still not convinced having a separate dab page is necessary since the tesseract and hypercube graph articles are linked from that page anyway. —David Eppstein 18:29, 15 November 2006 (UTC)

I agree with David Eppstein. The mathematical community does not mean 4-dimensional when it says "hypercube". I do believe the name "hypercube" has been used, e.g. in science fiction, for the 4-cube, and it would be good to give that as a secondary meaning with a link to tesseract.

Here's a suggestion: Keep "hypercube" as a disambiguation page, since there are several meanings, such as the graph. Create hypercube (geometry) to move measure polytope to. Put into measure polytope a short definition as a unit hypercube (named by Coxeter, not common). I throw these ideas out for reactions. Let's hear! Zaslav 01:41, 16 November 2006 (UTC)

Hypercube, Hypercube graph, n-cube, and measure polytope are too closely related to be considered disambiguous. While the A_(disambiguation) article could be referring to a number of different completely unrelated concepts from many different fields. Same with the error page, it has a separate disambiguous page, however, hypercube only has one unrelated concept mainly the movie. The hypercube article will now contain what was once the measure polytope page, have a single disambiguous link to the movie at the top, and the article will refer to an n-cube when referring to a specific dimension, measure polytope should only be used when applied to hypercubes of unit length (side length, wrong terminology) one. --ANONYMOUS COWARD0xC0DE 00:23, 25 December 2006 (UTC)

Good! That's what I meant all along, really, really! (Also, the principal meaning of "hypercube" is obviously the geometrical one.) Thanks to whoever carried out the merge/move. Zaslav 06:40, 30 January 2007 (UTC)

[edit] Merge Hypercube<--Hypercube graph

To me it just seems that hypercube graph could be a section within Hypercube. Any dissenting view points? --ANONYMOUS COWARD0xC0DE 00:36, 10 January 2007 (UTC)

I don't see why a single merged article would improve the current situation, and I think the significant differences between hypercubes and hypercube graphs could make a merged article quite confusing. Hypercube graph lies in Category:Graphs, which may not be as relevant for hypercubes as geometric objects. There is also some important graph theory I hope to add but haven't yet concerning median graphs (retracts of hypercubes) and partial cubes (isometric subgraphs of hypercubes). A hypercube has faces of many dimensions while a hypercube graph has only vertices and edges. A hypercube is topologically equivalent to a ball while a hypercube graph has a large homology group. A hypercube has high dimension while the hypercube graph article talks about two-dimensional unit distance representations. We don't merge complete graph and simplex; why is this any different? —David Eppstein 07:41, 10 January 2007 (UTC)

Ok. I withdraw my request. --ANONYMOUS COWARD0xC0DE 04:51, 12 January 2007 (UTC)

[edit] "Measure polytope"

I changed the wording about and usage of this term, because a reading of Coxeter (1973) shows that he did not mean it to refer only to a unit hypercube. He meant it to be any "hyper-cube" (his spelling). Also, it seems clear to me, from his language, that he invented the name. Zaslav 17:41, 8 February 2007 (UTC)