@DavidHalitsky I have noticed that there is polytopes tag on MO. Maybe the tag would be suitable for some of your questions? (I have decided not to retag myself, since I am not familiar with this area of mathematics.)

There are some other tags containing the word polytopes, but they re probaly not related: convex-polytopes, abstract-polytopes, lattice-polytopes.

Since polytopes tag has 7 followers, this might improve chances (although only very slightly) that somebody familiar with this area might notice your question.

Still I will add a word of warning: Too much bumping is frowned upon, so if you decide to add the tag, you probably should not retag all your questions at the same time.

Thanks for ths suggestion Martin - much appreciated . . .

@MartinSleziak - your observation about tags helped me to crystallize my thinking about something, and as a result, I posted this question at metaMSE math.meta.stackexchange.com/questions/27739/…

> So, here's my question: should MSE have a "distinguished" class of questions which can be tagged "cross-specialty", in order to alert people that a question requires consideration by more than one kind of specialist at MSE?

Isn't simply the fact that a question is tagged with tag from various areas indication enough that it is - to use your terminology - cross-specialty?

From what I read on meta before, I think Jyrki Lahtonen has very reasonable opinions and his posts are often very well thought-through. So we will what he has to say about this.

@MartinSleziak Hi Martin. This is not actually a reply to your message, rather an appeal for help. You may have explained to me before how to quote (or import, whatever the correct verb is) a large chunk of text into a chat room. In any case, I'd like to quote the entirety of Richard's meta post, as it has two votes to delete but may be useful for participants here. Thanks.

@ToddTrimble I doubt that there is easy way to do this. But since this seems to be related more to "how to do something to chat" rather than to this specific discussion, maybe we could continue this elsewhere if you agree.

well, as it is still on hold, there is no way to answer it online.
And for adding a comment there, I have not enough MO-reputations so far.

But your rewording of your question is rather obvious!
An 8D simplex aka enneazetton has
9 vertices
36 edges
84 triangles
126 tetrahedra
126 pentachora
84 hexatera
36 heptapeta
9 octaexa
for boundary elements. These numbers show up symmetrically because the enneazetton is selfdual, just as any regular simplex.

Further you mentions the dissection of the vertex set of the Gosset polytope 4_21 according to 240 = 84+72+84. This is based on the fact that 4_21 can be described as the convex hull of 2 mutually inverted copies of a birectified enneazetton (each 84 vertices) and one expanded enneazetton (72 vertices).

Your question about the occurance of 84 in both these statements is indeed closely related.
Reconsider the eneazetton x3o3o3o3o3o3o3o. The rectified enneazetton o3x3o3o3o3o3o3o therefrom is derived (up to some global scaling) as the convex hull of the center of the edges of the simple eneazetton. Likewise the birectified enneazetton o3o3x3o3o3o3o3o can be derived from the simple eneazetton (up to scaling) as the convex hull of the centers of its triangular faces. In fact, this series not only goes on in right this manner wrt. this special polytope, it rather is valid for all convex regular …

That is, because of 84 is the number of triangles of the eneazetton, thus the birectified eneazetton would have 84 vertices. And because of the birectified eneazetton is vertex inscribable into the Gosset figure 4_21, that very number reoccurs there too.

That’s it.

@ToddTrimble I am not sure whether the above is approximately what you wanted to get. I do not have better other than posting it in separate messages.

Since you are a mod, you should be able to delete my messages if you want to get rid of them and you should be able even to edit them. (Regular users are able to edit their messages only for a short time after the message is posted.)

Alternatively, any room owner can move the messages away. (So in the case the messages should be removed, they can be simply moved to trash.

And, of course, they can also be moved to the other room: Discussion on question by David Halitsky: $E_6$, $E_8$, and Coxeter's (anti-)prismatic projections of the n-dimensional cross-polytopes

@MartinSleziak Thanks for doing this, and sorry for the extra work. I thought maybe there was a simpler means that you knew of. But this is certainly fine; thanks again.

@ToddTrimble Well it seems that the whole thing can actually be posted as a single message: chat.stackexchange.com/transcript/message/42336130#42336130

I am actually surprised by that, since I thought that if I post it as a single message I get "message is too long" error.

I have learned something new about chat today. :-)

@ToddTrimble In any case, I'd consider the issue of copying the post into chat basically solved. So we might leave this room for its original purpose - and if some further discussion related to how to do something in chat is needed, we might continue it elsewhere.