Talk:4 21 polytope

Drawing
Reference drawing from McMillian of E8 and E7: File:E7-8 graphs.png - SockPuppetForTomruen, 01:43, January 6, 2010‎

Confusing
This is an example of an article which needs to be made to conform to WP:MSM. I am tagging it as such and I will make an attempt at it. Orange Knight of Passion (talk) 23:29, 13 September 2008 (UTC)

I tried, but the intro still refers to "all permutations of rings in this Coxeter-Dynkin diagram" which is really unclear and confusing for the WP:LEAD. But technically this is still a stub, so I guess it's okay for now. Orange Knight of Passion (talk) 23:54, 13 September 2008 (UTC)


 * Yes, I know pretty bad, sorry. I'm still fleshing out the stub articles to make sure I have the right numbers, and hoped others could help too. I've got a number of books, but its hard to write much until I understand more, what's significant, and what can be explained usefully and simply. ANYWAY, I reworked a bit, hopefuly a little better. Tom Ruen (talk) 23:01, 14 September 2008 (UTC)


 * Much better. The only way I can see to improve is to wiki link the jargon terms (e.g., "semiregular" -- for math articles math jargon is usually words with a very precise and specific meaning.)  I don't have the necessary reference sources to proofread the numbers unless I go to a library.  Isn't it more important to have descriptions of the lists and tables in Uniform polytope along with keys for the symbols? Orange Knight of Passion (talk) 15:41, 16 September 2008 (UTC)

Lisi theory -> "E8 theory"
At Talk:An_Exceptionally_Simple_Theory_of_Everything some editors apparently not acquainted with E8 in other contexts are proposing to move that article to "E8 theory", which I feel would be ambiguous and giving Garrett Lisi's theory excessive weight. Please come and help discuss this. --JWB (talk) 03:56, 26 November 2009 (UTC)

3D projections vs. Folding of Zome model of concentric 600 cells
Not sure why the Zome physical model (vs. the 3D mathematical model of the exact same thing) warrants moving to a "folding" area. Move both or none. BTW - I am concerned and working to find the precise 4D projection basis for justification of folding. I have the full 2D and 3D basis vectors, but the 4D basis seems to be a problem w/only 56 of 120 vertices projected given the permutations of +/- 1 & phi. Jgmoxness (talk) 01:33, 14 February 2012 (UTC)


 * Sorry, I find the "3d mathematical mode" views confusing, hopelessly cluttered by edges, while the simplified zome model a bit more clear, so I was being hopeful it could fit within the folding section. The paper Affine extensions of non-crystallographic Coxeter groups induced by projection, figure 1, seems to contain the folding with two projective root lengths. So anyway, I moved the 3D image hoping for a higher dimensional comparison than the Coxeter planes, but they all seem too cluttered to me. p.s. If I remember right, Ritcher's Zome model is the 4D coordinates with one axis dropped. Tom Ruen (talk) 02:25, 14 February 2012 (UTC)
 * Yes, Richter's model uses two concentric 600 Cells coordinates (one scaled by Golden Ratio) and drops one axis. That is what the math model is as well. I could make a math model with the same edge set as Zome, but then it would look exactly the same and provide no added value. Of course, it is physically imposssible to make a Zome model with even 3360 edges (but I could create one via 3D printer and take a picture). My model shows only the 3360 shortest edges (and excludes the second set of 3360 edges needed for an E8 fold - that was too cluttered).
 * My issue relates to getting E8 coordinates (e.g. split real even) to project to H4 using 4 basis vectors. Don't confuse constructing the 3D Zome from Cell 600 vertices as proof of it folding from E8. What I have proven is I can construct the 2D and 3D projections of H4 from E8 projections using 2 and 3 basis vectors! But haven't succeeding in doing that with 4. I too looked at the referenced paper. It seems Eq. 3 does NOT project E8 to H4 (Cell 600) as described - at least not using the split real even construction.

Jgmoxness (talk) 13:38, 14 February 2012 (UTC)

attempted to fix explanation of Coxeter diagram for the vertex figure
I changed this explanation to

"The vertex figure is determined by removing the ringed node and making its neighboring node into the ringed node."

which seems to match what was actually done to get the Coxeter diagram for the vertex figure. The original text mentioned the "red node", and was unclear to me in other ways too.

Please fix my explanation if it's wrong.

6-simplexes?
User:John Baez, this source,, says 138240+69120 6-simplex faces. The new paragraph, edit, is doubled this on the second number. Tom Ruen (talk) 02:36, 10 December 2014 (UTC) User:Aschheim, this source,, says that every 7-simplex has 8 6-simplex facets, and not 7 as in the computation which seems to conduct to a false result. The number of 6-simplex is 207360 = 1/2 (17280 * 8 + 2160 * 128) = 138240 + 69120 as in your reference. If you agree with this we (you or me) can correct the paragraph. —Preceding undated comment added 16:01, 25 November 2015 (UTC)
 * I'm not sure I completely follow, but agree this looks like an error "Since every 7-simplex has 7 6-simplex facets", should say "Since every 7-simplex has 8 6-simplex facets". Tom Ruen (talk) 16:47, 25 November 2015 (UTC)

Unfortunate use of the word "node"
Usually the word "node" means a marked point of some kind. Coxeter-Dynkin diagrams already have marked points, often called "nodes".

And usually when a marked point in a Coxeter-Dynkin diagram has a circle around it, the circle is called a "ring" and that point (node) is said to be "ringed" (pronounced as one syllable with a hard G and a silent E).

So: The use of the word "node" to denote "a ring around a node" is particularly confusing here.2600:1700:E1C0:F340:5C3C:4E22:904D:5D29 (talk) 21:33, 16 December 2018 (UTC)