Re: Hexany Article

Members may like to know that they decided to keep my hexany article on wikipedia:

http://en.wikipedia.org/wiki/Hexany

:-)

Robert

Hooray!

--- In tuning@yahoogroups.com, "Robert walker" <robertwalker@...> wrote:
>
> Members may like to know that they decided to keep my hexany
> article on wikipedia:
>
> http://en.wikipedia.org/wiki/Hexany
>
> :-)
>
> Robert
>

Hi Carl,

You may also like to know, the eikosany's geometric figure has just been identified as the "birectified 5-simplex".

http://en.wikipedia.org/wiki/Talk:Hexany
http://en.wikipedia.org/wiki/Hexany#Coordinates_for_the_Pascal.27s_triangle_of_combination_product_sets

Robert

--- In tuning@yahoogroups.com, "Robert walker" <robertwalker@...> wrote:
>
> Hi Carl,
>
> You may also like to know, the eikosany's geometric figure has
> just been identified as the "birectified 5-simplex".

Did you miss the message here where I identified it as the
uniform dodecatetron?

-Carl

Hi Carl,

I saw that message, but can't use it in Wikipedia as I could find no references to it - web search for "uniform dodecatetron" doesn't turn up anything apart from your tuning posts - nor does dodecatetron on its own, and you didn't give any references.

The birectified 5-simplex only turns up two pages - but it is a compound of two names that are in common use, just like e.g. rectified 111-simplex or whatever, which probably isn't mentioned anywhere but if you ever needed to work with one that's what you would call it. And it fits the description..

It's possible that the uniform dodecatetron is the same thing as the birectified 5-simplex since many of the shapes have multiple names, with a "common name" for the ones that are special enough to need separate names, in the lower dimensions especially and 5 dimensions is low enough so that it may well have a "common name" amongst researchers working in five dimensions.

If you think it might be - or just wonder if perhaps it is the same thing (there may be many shapes with 20 vertices and triangular faces for instance), why not post about it to the talk page of the hexany? Seems it's quite a good way to find out answers - as the page obviously gets a fair number of mathematicians visiting it - most of the reviewers of the Keep decision were maths professors I found by looking up their user pages, and one of them may know the answer.

Thanks,

Robert

> Did you miss the message here where I identified it as the
uniform dodecatetron?

--- In tuning@yahoogroups.com, "Robert walker" <robertwalker@...> wrote:
>
> Hi Carl,
>
> I saw that message, but can't use it in Wikipedia as I could
> find no references to it - web search for "uniform dodecatetron"
> doesn't turn up anything apart from your tuning posts - nor does
> dodecatetron on its own, and you didn't give any references.

As I thought I said, that information was provided by George
Olshevsky on this list years ago. His e-mail on the subject
has been posted to this list at least twice.

> It's possible that the uniform dodecatetron is the same thing
> as the birectified 5-simplex since many of the shapes have
> multiple names,

Yes.

> If you think it might be - or just wonder if perhaps it is the
> same thing (there may be many shapes with 20 vertices and
> triangular faces for instance), why not post about it to the
> talk page of the hexany? Seems it's quite a good way to find
> out answers - as the page obviously gets a fair number of
> mathematicians visiting it - most of the reviewers of the
> Keep decision were maths professors I found by looking up
> their user pages, and one of them may know the answer.

I trust Olshevsky more than "Tamfang", especially when
the latter is saying "possibly" and the when the former
was even able to catch a mistake Paul E. made on one of
the vertices.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Robert walker" <robertwalker@>
> I trust Olshevsky more than "Tamfang", especially when
> the latter is saying "possibly" and the when the former
> was even able to catch a mistake Paul E. made on one of
> the vertices.

Olshevsky is the master of polyhedra.

He lives here in San Diego. I enjoyed a nice afternoon
with him at a coffee-shop, as he drew 5-diminsional
polyhedra by hand on a napkin. What a genius.

He likes dinosaurs too.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

Hi Carl,

Okay that's enough for a note on the talk page. But I don't feel it's enough to add it to the article without more information from Olshevsky himself and a reference to where one can find out more about the name, what it means (why is it called a uniform dodecatetron), and who uses the name.

It's obviously uniform. But why "dodecatetron"? What does the dodeca part refer to and what is a "tetron"? Is it in a family with other shapes with simliar names, if so where can one go to look up and read about them if anyone reading the article wants to find out more about the subject?

With the birectification, I'm not relying on the note from "Tamfang". He just gave the hint I needed to see that it is the 2D face dual of the 5-simplex. That's then obvious from the way it is constructed. In the 6-dimensional hypercube, scale everything by a factor of 1/3 about the origin, and the vertices of the eikosany move to the centres of the faces of the 5-simplex. For instance, 11100 moves to the mid point of the equilateral triangle with coords 10000, 010000, 00100. Simlarly for all the vertices of the eikosany.

So that means that the eikosany just _is_ the 2D face dual of the 5-simplex. It's a matter then of what you call that. Birectified is what it is called in the Wikipedia article on rectification, so, with no other name available to use, that's what I called it. I can't find that much on birectification on the web, but then it is a fairly rare thing to want to do, and I can't find an alternative name for it either.

Do you want me to add the note for you?

-Carl

Hi Carl,

I thought the best thing was to e-mail George Oshlevsky directly - found his web site and home page through his entry in Wikipedia. So I've done that and asked my questions about the name from my previous post.

So - will see what he says. I also invited him to edit the article of course.

Robert

you might have him look at the hebdomekontany article
http://anaphoria.com/HEBDOa.PDF

Robert walker wrote:
>
> Hi Carl,
> > I thought the best thing was to e-mail George Oshlevsky directly - > found his web site and home page through his entry in Wikipedia. So > I've done that and asked my questions about the name from my previous > post.
> > So - will see what he says. I also invited him to edit the article of > course.
> > Robert
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

Thanks, will do.

He has just replied answering my questions BTW - teron means 4D face, derived from greek tetron, and so dodeca refers to the twelve dekany faces of the eikosany. It's unofficial as he doesn't think it has been published anywhere - has become current amongst fellow researchers into higher polytopes, not "set in stone". But looking on wikipedia, "teron" seems to be used a fair bit (though no results for dodecateron anywhere). Also they used to call them "tetron"s but now call them "teron"s because of some ambiguity in 10 dimensions or higher - not sure about that point as I need to ask him what he means.

Anyway I had a couple more questions for him, and will prob. update the article with a note about it all (or in the talk page), so will see what he says about the hebdomekontany at the same time.

Thanks.

Robert

you might have him look at the hebdomekontany article
http://anaphoria.com/HEBDOa.PDF