Talk:Hexany

message: Combination product sets are common parlance amongst modern microtonal theorists interested in just intonation tunings and musical lattices. I'm sure there must be more articles published on them.
Can anyone help add more references? 
One of the basic notions of the field along with Moment of Symmetry etc.
Robertinventor (talk) 19:08, 7 February 2008 (UTC)
thread_title: AfD discussion request for help

message: Does anyone know the name for the geometrical figure whose vertices are the vertices of the Eikosany (five dimensional figure with 20 vertices)?
Robertinventor (talk) 19:08, 7 February 2008 (UTC)
replies: text: possibly birectified 5-simplex. —Tamfang (talk) 19:14, 16 February 2008 (UTC)

text: Thanks! That's obviously right, I'll edit the page, accordingly. Robert Walker (talk) 10:07, 17 February 2008 (UTC)

text: On second thought I'd prefer a more abstract birectified hexatope. —Tamfang (talk) 18:48, 6 June 2010 (UTC)
thread_title: geometrical name for figure with the Eikosany vertices

message: I think I understand what the article is getting at, but for a reader without a strong grasp of combinatorics it must be baffling.
* It's not really about the "hexany" but about its generalizations and supersets.
* If frequencies are to be wrapped into an octave, why have 2 as an axis of the hypercube?
* If we must have the hypercube, wouldn't it be simpler to choose (0,0,0,0) aka "1" as one of the corners of the octahedron?  If not, say why not.  Perhaps you could explicitly list the four octahedra derived from the hypercube.
* Nobody needs an explicit list of all the strings of n bits.
* Are the higher-dimensional examples for harmonies with more primes, or what?
* The passage about Pascal's triangle is obscure.
—Tamfang (talk) 03:37, 26 January 2009 (UTC)
thread_title:  huh? 

message: I just realised that informal proof isn't quite complete. Also - perhaps it counts as "original research".
It could still be a "folded octahedron" - a 3D object folded in 4D - like folding a perfect 2D square along its diagonal in 3D.
You can see that the octahedron's three equatorial "squares" have opposite sides parallel which means that they can be drawn within a 2D space - still that doesn't prove that the angles at the vertices have to be all the same, but by the symmetry of the hypercube then there is no reason for any angle to be larger than any other - so I think they have to be squares.
So - with equatorial squares (surely), and all edges exactly the same length, it seems pretty likely that it is a perfect octahedron, to me - but still not sure how you prove it rigorously. If it is a perfect octahedron then you should be able to show that there is a 3D slice of the hypercube which has all of its vertices included within it. Vice versa if you can show that then it proves it really is a perfect octahedron.
Part of it is that I am a bit out of practise with maths, have been programming for many years now and only done occasional maths for perhaps about 15 years or more. Perhaps some of you reading this who are active mathematicians can see this more easily than me. Also is there any reference - that's best of all if someone somewhere has published a proof that it is a perfect octahedron so it is not OR though for simple maths that anyone could follow not sure it really counts as OR.
Robert Walker (talk) 21:58, 27 November 2012 (UTC)
replies: text: You can prove it is perfectly symmetrical because all the points are equally distant from the 0 point so they are all in the same 3D plane and then, all are equidistant from each other so must be a perfect octahedron in 3D. Robert Walker (talk) 18:23, 5 February 2017 (UTC)
thread_title: Proof that it is a regular octahederon when embedded in the hypercube

message: I wrote this as an article about Combination Product Sets so what I describe here is the hexany as a 2)4 CPS. 
But the 3D hexany also occurs in 3D of course as someone has just commented off wiki about this page I talk about the 3D hexany here on my own website :) in cubic lattices 
So just leaving this as a note for now. It obviously needs to be updated to mention this. I just forgot to say and nobody else seems to have noticed the omission in all this time. But the article should continue to present the hexany as a 2)4 (2 out of 4) CPS set. After all that's where the idea originated and it's part of the progression of CPS sets to higher dimensions, the dekanies etc. Robert Walker (talk) 17:27, 5 February 2017 (UTC)
thread_title: Doesn't mention that the hexany also occurs in 3D e.g. in the cubic lattice 

message: the two later section after tuning do not relate to the hexany and i deleted some time back only to see it put back in. It does not even make logical sense. it speaks about the dekany in language that is impsosible to understand. the writer does not understand what they are talking about. It is slander and an attempt to undermine the understanding of it which is quite simple. — Preceding unsigned comment added by Banaphshu (talk • contribs) 05:26, 17 February 2024 (UTC)
replies: text: I agree that the last two sections (relating to Pascal's triangle) are impossible to understand and add nothing useful to the article. DaveSeidel (talk) 14:14, 17 February 2024 (UTC)
replies: text: Removed. The rest of the article is still somewhat lacking in intelligibility. —David Eppstein (talk) 17:54, 17 February 2024 (UTC)
thread_title: Extraneous material