Talk:Rectified 600-cell

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There are five uniform polychora of 720 cells (truncated, rectified, and bitruncated 120- and 600-cells), so how does this one get to be "the 720-cell"? Is it special because all its faces are triangles? —Tamfang 04:22, 7 February 2006 (UTC)

Hi Anton,

Good catch, no defence. I changed it. I originally titled the article 720-cell needing a name. I renamed the article later, but forgot to change the references in the article.

Incidentally, the dual of the Rectified 600-cell ALSO has 720 cells AND it is perhaps more impressive for being cell-uniform!

Tom Ruen 06:16, 7 February 2006 (UTC)

That reminds me, someday I mean to make 47 vertex figures (stick-style, so they should be easier to read than Dinogeorge's) and their duals. —Tamfang 18:23, 7 February 2006 (UTC)

I've also been wanting to create images of the polychora projected into 3-space. Unfortunately, after next week I will have no time to do this. What do you guys think of this idea, though? I've always preferred 3D projections over the line-diagrams used in many of the current polychora pages. Maybe when I get time again I'll try to whip something up using povray.—Tetracube 00:52, 8 February 2006 (UTC)

I've got a program that can generate uniform polychora (or the subset with mid-edge reflection symmetry), not tested all of them yet to see which ones I can generate. (other symmetries are also possible for me to generate, but a step further).

My goal is to generate more of the Andreini_tessellation first, since they are the same idea as uniform polychora and they really exist in 3-space. Unfortunately I'm unsure when I can spend a big enough chunk of time on it, so it could be months for me as well.

On polychora, I admit I don't have a good idea of a best representation in 2D images. I'm content to start with wireframes with an orthogonal projection, then try wire-frames with perspective, then solid/semi-transparent faces like hypercube, then maybe cross-sectional pieces like Jonathan Bowers does. And of course there's "nets" as well, vertex figure nets AND full nets. Examples: [1]

I perhaps support "borrowing" Bowers cross-section images into Wikipedia directly, and from emailing, he has seemed open to that possibility I think: Bowers old and Bowers new and [2]

—Preceding unsigned comment added by Tomruen (talk • contribs) 18:07, 7 February 2006

Personally, I dislike cross-sections, because it is very difficult to visualize the object given a set of cross-sections. It does make for a pretty picture, though, so maybe it's good enough. I also definitely prefer cells with transparent faces, otherwise you only get see the silhouette of the 4D object with no information about where the images of the cells lie. Nets are interesting in their own right, although I consider them secondary.—Tetracube 07:06, 8 February 2006 (UTC)