I mostly added the resource template because I'd like sources for this name. Tom Ruen 00:55, 29 July 2006 (UTC)
Where did all these -teron, -peton, etc. names come from? Who first called them that? I'm a little suspicious because dodecapeton, for example, gets zero Google hits. — Keenan Pepper 04:38, 4 September 2006 (UTC)
Seems like this comes from Wendy Krieger. Not something that belongs in Wikipedia, but something that has gathered some amateur use. – OfficialURL ( talk) 02:22, 13 May 2020 (UTC)
I've heard n-cube used, but the existing article at n-cube seems to be something different. Tom Ruen 00:45, 4 November 2006 (UTC)
I am a mathematician and I often refer to the n-cube or hypercube. I never heard of a "measure polytope". The common name for this geometrical object is hypercube or n-cube. If anything is merged, this article should be merged into n-cube, not the other way round. However, I recommend the name "hypercube" as an article title, since that is the most correct general name. (n-cube means a specific dimension, n. Hypercube does not specify the dimension, so it's the most general.) Zaslav 17:51, 15 November 2006 (UTC)
My own resistance against using hypercube as naming the family is that the name implies "beyond the cube", so it would seem to exclude the lower elements.
There's also the dual family, cross-polytope to consider. Do you have a shorter name for that? I've heard people use n-diamond (in the "baseball" diagonal sense) perhaps?
Tom Ruen 00:08, 16 November 2006 (UTC)
Matches in MathSciNet for "hypercube": 2014. Matches in MathScinet for "measure polytope": 5. Matches in Google Scholar for "hypercube": 77600. Matches in Google scholar for "measure polytope": 36. I am quite confident that the majority of matches for hypercube in both cases do not restrict themselves to exactly four dimensions. — David Eppstein 01:50, 16 November 2006 (UTC)
I surrender but not on search results implying dimensions of meaning. It still seems wierd that "cube is a geometric object" and "hypercube is a class of geometric objects". Simplex has the same problem, but we don't talk about hypertriangles to imply simplices of any dimension! At least Coexter is consistent with his notation - adding "tope" suffix to objects of general dimension.
I questioned "cross-polytope" because I considered it in the same category as "measure polytope" - a slightly clumsy term for a class of objects.
I am most comfortable with n-cube since it is a clear set rather than an object. There's still the n-cube article of little discussion and minimal edits, added anonymously ONCE, touched a couple times.
How about:
Tom Ruen 04:17, 16 November 2006 (UTC)
I can understand taking the cube, and sweeping it such that we get this picture Hypercube. What I don't understand, is what this picture is supposed to represent Confusing Hypercube
I kind of understand it now, although isometric projections are easier to understand that perspective projections. Thanx
Paskari
19:57, 30 November 2006 (UTC)
I mostly added the resource template because I'd like sources for this name. Tom Ruen 00:55, 29 July 2006 (UTC)
Where did all these -teron, -peton, etc. names come from? Who first called them that? I'm a little suspicious because dodecapeton, for example, gets zero Google hits. — Keenan Pepper 04:38, 4 September 2006 (UTC)
Seems like this comes from Wendy Krieger. Not something that belongs in Wikipedia, but something that has gathered some amateur use. – OfficialURL ( talk) 02:22, 13 May 2020 (UTC)
I've heard n-cube used, but the existing article at n-cube seems to be something different. Tom Ruen 00:45, 4 November 2006 (UTC)
I am a mathematician and I often refer to the n-cube or hypercube. I never heard of a "measure polytope". The common name for this geometrical object is hypercube or n-cube. If anything is merged, this article should be merged into n-cube, not the other way round. However, I recommend the name "hypercube" as an article title, since that is the most correct general name. (n-cube means a specific dimension, n. Hypercube does not specify the dimension, so it's the most general.) Zaslav 17:51, 15 November 2006 (UTC)
My own resistance against using hypercube as naming the family is that the name implies "beyond the cube", so it would seem to exclude the lower elements.
There's also the dual family, cross-polytope to consider. Do you have a shorter name for that? I've heard people use n-diamond (in the "baseball" diagonal sense) perhaps?
Tom Ruen 00:08, 16 November 2006 (UTC)
Matches in MathSciNet for "hypercube": 2014. Matches in MathScinet for "measure polytope": 5. Matches in Google Scholar for "hypercube": 77600. Matches in Google scholar for "measure polytope": 36. I am quite confident that the majority of matches for hypercube in both cases do not restrict themselves to exactly four dimensions. — David Eppstein 01:50, 16 November 2006 (UTC)
I surrender but not on search results implying dimensions of meaning. It still seems wierd that "cube is a geometric object" and "hypercube is a class of geometric objects". Simplex has the same problem, but we don't talk about hypertriangles to imply simplices of any dimension! At least Coexter is consistent with his notation - adding "tope" suffix to objects of general dimension.
I questioned "cross-polytope" because I considered it in the same category as "measure polytope" - a slightly clumsy term for a class of objects.
I am most comfortable with n-cube since it is a clear set rather than an object. There's still the n-cube article of little discussion and minimal edits, added anonymously ONCE, touched a couple times.
How about:
Tom Ruen 04:17, 16 November 2006 (UTC)
I can understand taking the cube, and sweeping it such that we get this picture Hypercube. What I don't understand, is what this picture is supposed to represent Confusing Hypercube
I kind of understand it now, although isometric projections are easier to understand that perspective projections. Thanx
Paskari
19:57, 30 November 2006 (UTC)