User:Tomruen/archive2

Archive 2

2008 comments

WTF explanation

Tom, I was in the middle of editing Talk and the subhead got screwed up. This was about the mention of "single vote" in the introduction, not about the explanation of what "instant runoff means." this is all summarization of the RFC, since MilesAgain is editing based on his imagination of what the seriously defective RFC meant. (He asked three questions, then answered them with a single "Yes," causing all kinds of ambiguity in the subsequent discussion, as three distinct questions got all mixed up. That *might* be what he wants, I might suspect, but that would be WP:ABF though I don't have a lot of trouble with that assumption with sock puppets. Sorry for the confusion. --Abd (talk) 04:57, 8 January 2008 (UTC)

I'm grumpy all around, least of all the confusion on the IRV talk page. I think your view is wrong. Single-transferable-vote is a darn good name for IRV, and applied to IRV outside the U.S. for single winner elections. However you want to word it, single vote deserves PRIME attention in the IRV intro. I can say no more without getting more frustrated, and I'm staying out of editing. Tom Ruen (talk) 05:51, 8 January 2008 (UTC)

Image:2-cube column graph.gif listed for deletion

An image or media file that you uploaded or altered, Image:2-cube column graph.gif, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. —PNG crusade bot ^(feedback) 22:32, 11 January 2008 (UTC)

Császár polyhedron

Hi! Would you like to try and make some image (or even an animation) of this strange polyhedron? I found some images here and there, and it seems quite a difficult job. Thanks --Zio illy (talk) 14:43, 19 January 2008 (UTC)

Sounds interesting, and agreed hard, even if I had the vertex-edge-face data, to draw a single perspective that shows much what it is. I must hold off now, but tell me if you find any data for it! Tom Ruen (talk) 01:06, 20 January 2008 (UTC)

IRV implementations in United States

Dear Tom Ruen, we already have an article on the history and use of instant-runoff voting in the United States. I recommend that this article and your article (IRV implementations in United States) should be merged. Markus Schulze 17:52, 26 January 2008 (UTC)

Hi Markus. I realized, but it seemed ignored and so it was easier to MOVE material from the main article than merge, so I'm happy if anyone else wants to sort this out. I was just trying to get the details off the main article.

Speedy deletion of Template:Uniform dual polyhedra db

A tag has been placed on Template:Uniform dual polyhedra db requesting that it be speedily deleted from Wikipedia. This has been done under section T3 of the criteria for speedy deletion, because it is a deprecated or orphaned template. After seven days, if it is still unused and the speedy deletion tag has not been removed, the template will be deleted.

If the template is intended to be substituted, please feel free to remove the speedy deletion tag and please consider putting a note on the template's page indicating that it is substituted so as to avoid any future mistakes (<noinclude>{{transclusionless}}</noinclude>).

Thanks. --MZMcBride (talk) 21:25, 19 February 2008 (UTC)

I don't care if its deleted now, as long as I can recreate it when I get around to using it. Thanks! Tom Ruen (talk) 21:27, 19 February 2008 (UTC)

Speedy deletion of Template:Uniform dual tiles db

A tag has been placed on Template:Uniform dual tiles db requesting that it be speedily deleted from Wikipedia. This has been done under section T3 of the criteria for speedy deletion, because it is a deprecated or orphaned template. After seven days, if it is still unused and the speedy deletion tag has not been removed, the template will be deleted.

If the template is intended to be substituted, please feel free to remove the speedy deletion tag and please consider putting a note on the template's page indicating that it is substituted so as to avoid any future mistakes (<noinclude>{{transclusionless}}</noinclude>).

Thanks. --MZMcBride (talk) 21:26, 19 February 2008 (UTC)

Thanks!

I just wanted to thank you for the Eclipse page. Its really cool, and well done. Keep up the good work. 67.188.118.64 (talk) 03:25, 21 February 2008 (UTC)

Your interspersed Talk edit

Tom, you made an interspersed Talk response with [1]. I used to be tempted to do that kind of thing because of my history with mailing lists, where interspersal in a reply is often very good; however, here, what serves as the effective primary record of a discussion gets cut up, making it more difficult to follow who is saying what. If it is justified, the prior section really should have a sig added to it (copy of the original), and a note that it is continued below). Instead, if I really need to respond to something point by point, I have adopted the practice of quoting it, often with italics to set it off. See Wikipedia:Talk page guidelines#Editing comments and specifically:

Interruptions: In some cases, it is OK to interrupt a long contribution, either by a short comment (as a reply to a minor point) or by a headline (if the contribution introduces a new topic). In that case, add "<small>Headline added to (reason) by ~~~~</small>"). In such cases, please add {{subst:interrupted|USER NAME OR IP}} before the interruption.

--Abd (talk) 20:07, 21 February 2008 (UTC)

Abd, I think we should come up with a template for letting people know about this whole interspersed editing thing. In fact, I'm going to be bold and do it right now! The new template is Template:Intersperse, and it takes one parameter, e.g. {{intersperse|Talk:IRV_implementations_in_United_States}}. See below for example:

Ron Duvall (talk) 20:35, 21 February 2008 (UTC)

Sorry - Template sounds useful, although I was just copying Abd's old bad behavior! :) Tom Ruen (talk) 21:38, 21 February 2008 (UTC)

Copy my good behavior, not my bad! I'll try to do the same with you... okay? --Abd (talk) 22:07, 21 February 2008 (UTC)

Shoulders of giants

Did you know that Sir Isaac Newton's famous humble-pie quote "If I have seen further, it is by standing on the shoulders of giants" was actually written to a dwarf scientist named Robert Hooke and clearly meant as an insult? Ron Duvall (talk) 23:28, 21 February 2008 (UTC)

Yeah, I'm a mean-spirited person too! The ideal insults ought to be constructed so as to never to be recognized... :) Tom Ruen (talk) 23:35, 21 February 2008 (UTC)

symmetry

I didnt find out what I was looking for. I wanted to know how many lines of symmetry a cuboid has! —Preceding unsigned comment added by 172.142.75.157 (talk) 14:27, 1 March 2008 (UTC)

Image:E8_graph2.svg listed for deletion

An image or media file that you uploaded or altered, Image:E8_graph2.svg, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Nv8200p talk 17:11, 10 March 2008 (UTC)

Hello

I've seen your important contributions for the article Exact trigonometric constants. I'm looking for the general (non-iterative) non-trigonometric expression for the exact trigonometric constants of the form: ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ , when n is natural (and is not given in advance). Do you know of any such general (non-iterative) non-trigonometric expression? (note that any exponential-expression-over-the-imaginaries is also excluded since it's trivially equivalent to a real-trigonometric expression).

Let me explain: if we choose n=1 then the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes "0", which is a simple (non-trigonometric) constant. If we choose n=2 then the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes ${\begin{aligned}{\frac {1}{\sqrt {2}}}\end{aligned}}$ , which is again a non-trigonometric expression. etc. etc. Generally, for every natural n, the term ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ becomes a non-trigonometric expression. However, when n is not given in advance, then the very expression ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ per se - is a trigonometric expression. I'm looking for the general (non-iterative) non-trigonometric expression equivalent to ${\begin{aligned}\cos {\frac {\pi }{2^{n}}}\end{aligned}}$ , when n is not given in advance. If not for the cosine - then for the sine or the tangent or the cotangent.

Eliko (talk) 07:26, 31 March 2008 (UTC)

Hi, interesting question. Obviously it can be computed for a given n, by half angle identities. If we looked at: cos(45 deg), cos (22.5), cos(11.25), cos(6.625), probably we'd see a sequence of ever deeper nesting radicals. I'm not sure what you mean by non-iterative. I wouldn't expect the radials could be simplified further in general, but I don't know. Tom Ruen (talk) 15:00, 31 March 2008 (UTC)

By "non-iterative formula" I mean: closed formula. Anyways, thank you for your answer. Eliko (talk) 14:09, 1 April 2008 (UTC)

Guess What!

	The Regret Tenenbaum Seal of Approval
	Holy Crap! You were awarded the The Regret Tenenbaum Seal of Approval for being so awesome! - Regret Tenenbaum (talk)

Bowers style acronym

Why you removed Bowers style acronym [2] ? Maksim-e (talk) 18:37, 3 May 2008 (UTC)

Because the article Bowers style acronym was deleted. I figured better to hide the codes until some point they can be defended (like if they're referenced in a printed book someday.) SockPuppetForTomruen (talk) 21:40, 3 May 2008 (UTC)

Controversies regarding instant-runoff voting - delete nomination

I've nominated Controversies regarding instant-runoff voting for deletion. Please review and weigh in on this issue. QuirkyAndSuch (talk) 09:00, 13 May 2008 (UTC)

Compound of great icosahedron and great stellated dodecahedron

Compound of great icosahedron and great stellated dodecahedron is writen to be nr 61 at List of Wenninger polyhedron models, but not seems to be similar to it!

Compound of great icosahedron and great stellated dodecahedron	nr 61 at List of Wenninger polyhedron models

Maksim-e (talk) 17:55, 15 May 2008 (UTC)

It looks like both have a great icosahedron, but second doesn't have a great stellated dodecahedron, but hard to tell what it is... I'll have to look further. It's constructed from the stellation diagram in the book. SockPuppetForTomruen (talk) 01:02, 16 May 2008 (UTC)

great icosahedron

great stellated dodecahedron

Rhombic triacontahedron

Just a quick request/question. I recently converted Image:Rhombictriacontahedron net.png into an SVG image Image:Rhombictriacontahedron net.svg; however, the PNG version is still on Rhombic triacontahedron. Could you please fix this, as I have no clue how the template works! Thanks. --pbroks13^talk? 03:24, 23 May 2008 (UTC)

Done, changed at Template:Semireg dual polyhedra db. SockPuppetForTomruen (talk) 05:29, 23 May 2008 (UTC)

CO2 levels graph question

hey, just a question about your graph of CO2 levels over time, 650,000 years bp to now. The graph clearly decreases steadily several times, then jumps up. The decrease is always much slower than the increase. Also, the periods between increase and decrease are getting longer and the decreases and increases are increasing in amplitude. Why do you think this is? (the 3 things, I mean)? :)

Thanks for any response. It's an interesting graph, thanks. SpookyMulder (talk) 09:52, 24 May 2008 (UTC)

Hi Spooky. I basically only know it signifies the ice-ages, and correlates with average world temperature. CO2 itself increases generally with increased biological activity, so you might imagine less frozen land, more life, warmer oceans, more life, etc. There are theories that the ice age periods are related to periodic changes in the earth's oribit and axial tilt. On why the declines are slow and rise fast, my only guess is that once glaciers start to melt, they retreat relatively quickly (at least in geologic time), compared to forming? Anyway, my primary interest in the graph was to show named geological ice-ages as places in time, using the CO2 levels as a known absolute scale. It is very cool! SockPuppetForTomruen (talk) 17:51, 24 May 2008 (UTC)

Graph: Image:Atmospheric CO2 with glaciers cycles.gif

Algorithm for hypercube orthogonal projection

Hi, I'm trying to write a program to make SVG versions of your hypercube diagrams, like the one on the right. My program is starting to work, but I can't see what criteria you've used to decide which vertices get overlayed with each other to get the coloured dots. Is there some systematic arrangement to them that I'm missing, or are they decided by hand? If you've got code I could look at that would help. Thanks. --Qef (talk) 12:02, 6 July 2008 (UTC)

Basically I generated the vertices and edges of the unit hypercube, then defined a [u,v] basis to display an orthographic projection. I picked the U vector by the central direction of one vertex, and the V vector as an average direction of a set of vertices that define a path from the "one" vertex to the opposite vertex. Then I project V to be orthogonal to U, and that's my basis. The final step, I count how many vertices project to each position in the [u,v], plane and draw the circles different colors to show how many are overlapping.

The code is written in Borland Delphi. Here's the basis calculation: [view1,view2]

begin
  view1.copy(dim,cube.vert[1]);
  view1.scaleunit;
  view2.init(dim);
  v:=1;
  for i:=1 to dim do begin
    view2.add(cube.vert[v],1);
    v:=v*2;
    end;
  end;
  view2.add(view1,-view2.dot(view1)); // force view2 perpendicular to view1
  view2.scaleunit;
end;

Tom Ruen (talk) 21:26, 6 July 2008 (UTC)

I think I've finally figured out the maths for this. My program now produces something that looks correct. I've uploaded the 10-dimensional version (right).

The vertex colours don't exactly match the ones in the GIF versions. I'm using a palette of 11 colours extracted from the original 10-cube GIF diagram, hopefully in the right order (they're listed at the top of my source code), and I repeat them for higher numbers of overlayed vertices. If that's wrong or could be improved to be clearer, let me know.

The only other difference I can see is in my edge line widths. I'm using thicker lines to represent multiple edges drawn in the same place on the 2D image. I don't know how useful that is, but it gives a clearer impression of the large number of edges in higher dimension hypercubes.

What do you think? I'll hold off for a while uploading the other diagrams in case I've got something wrong.

--Qef (talk) 19:34, 23 July 2008 (UTC)

Hi Geoff. Very impressive. It looks good to me. You have my support to convert them all. Tom Ruen (talk) 20:13, 23 July 2008 (UTC)

Face-transitive vs. Isohedral

Tom, I have started a discussion at Talk:Face-transitive. Your input would be welcome. -- Cheers, Steelpillow (Talk) 19:38, 9 July 2008 (UTC)

Tenth stellation of icosahedron - and the rest

Tom, I have started a discussion here on the best way to handle the stellations of the icosahedron. Your contribution would be welcome. -- Cheers, Steelpillow (Talk) 10:00, 10 July 2008 (UTC)

Thanks for the pix. I have done a test table for the list. Have I missed anything? -- Cheers, Steelpillow (Talk) 09:21, 26 July 2008 (UTC)

Hi Guy. It looks good. I also got my copy of the book this week, so maybe I can help a bit, but a bit too busy this weekend. Tom Ruen (talk) 00:48, 27 July 2008 (UTC)

Oh, good. I can leave gaps in the table and not worry about them! I guess completing the set of 118 images will keep you busy for a while. -- Cheers, Steelpillow (Talk) 08:25, 27 July 2008 (UTC)

I have now merged in everything from other Wiki pages, and from the book's table of Wheeler and Bruckner. I won't have time to do nay more. Do you think it is fit to go live now, or do you want to fill in the rest first? -- Cheers, Steelpillow (Talk) 08:57, 29 July 2008 (UTC)

I think it's good enough to move to become an article, maybe as Fifty nine stellations of the icosahedron or The fifty nine icosahedra? I'm pulling myself in too many directions, but I'll try to add to it sooner or later, whether as your user subpage, or an article. Tom Ruen (talk) 18:14, 29 July 2008 (UTC)

Math notation style

Hello. Please see my recent edits to Petrie polygon and look at Wikipedia:Manual of Style (mathematics). Notice this difference:

2ⁿ-1

2ⁿ − 1

Spaces appear before and after the minus sign and the minus sign is longer than a mere hyphen. This matches TeX style. Generally in non-TeX math notation, variables, but not parentheses, braces, or other punctuation, should be italicized, a space should appear before and after "+", "=", "<", etc., and a minus sign should not be just a hyphen. I use "non-breakable" spaces with plus and minus signs but I don't worry that much about breakability with "=" and "<". Michael Hardy (talk) 22:20, 26 July 2008 (UTC)

Oh, and also, I've put in a commented out thing that says

, named after ????? Petrie,

If you know the name could you fill that in and then uncomment it? Michael Hardy (talk) 22:22, 26 July 2008 (UTC)

Thanks for the look. I added a statement about Petrie. I don't know if I have the patience for formatting, but I understand your changes. Tom Ruen (talk) 00:50, 27 July 2008 (UTC)

Regular 4-polytope

Welcome to Wikipedia. It might not have been your intention, but you removed a speedy deletion tag from Regular 4-polytope, a page you have created yourself. If you do not believe the page should be deleted, you can place a {{hangon}} tag on the page, under the existing speedy deletion tag (please do not remove the speedy deletion tag), and make your case on the page's talk page. Administrators will look at your reasoning before deciding what to do with the page. Thank you. andy (talk) 00:01, 11 August 2008 (UTC)

Sorry, I thought it was good. Tom Ruen (talk) 00:29, 11 August 2008 (UTC)

Net of truncated 600-cell

Hi TomRuen, your last revert of the net image removal to truncated 600-cell was mistaken: the net image was of the truncated 24-cell, not of the truncated 600-cell. (The net image has cubes and truncated octahedra as cells, which matches the truncated 24-cell, but the truncated 600-cell has icosahedra and truncated tetrahedra as cells instead.)—Tetracube (talk) 20:06, 11 August 2008 (UTC)

Thanks for fixing it. Tom Ruen (talk) 21:00, 12 August 2008 (UTC)

uniform polygons

Your last edit to Uniform polytope —

A uniform polytope must also have only regular polygon faces.

— reinforces exactly the false implication that I sought to remove! The regularity of the faces is a consequence of their uniformity (i.e. a polygon cannot be uniform without being regular), not an additional requirement. Can't we agree on a way to say it without "also"? —Tamfang (talk) 07:02, 14 August 2008 (UTC)

Sorry, do we need to divide the definition into two parts: (?)

A uniform polygon (n=2) must be regular.
A uniform n-polytope (n>2) requires (1) vertex-transitive (2) regular polygon faces.

Tom Ruen (talk) 15:20, 14 August 2008 (UTC)

... That's close to what George does on his definition: [3]

Uniform polytope: For n=2, a regular polygon. For n>2, a polytope whose facets are uniform polytopes and whose symmetry group is transitive on its vertices. Convex nonregular uniform polytopes are also called Archimedean polytopes, because it was Archimedes who first posed and solved the problem of finding all the convex polyhedra whose faces are regular polygons and whose vertices are “surrounded alike.” All regular polytopes are uniform, but because we have changed the restriction that the facets be regular to merely being uniform, most uniform polytopes are not regular.

Tom Ruen (talk) 16:52, 14 August 2008 (UTC)

The only reason I can see for separating the definition is to take some mystery out of it. "I know what regular polygons are, but what are uniform polygons?" "Well, they're all regular." "Why didn't you say so?" There's no inherent need to treat polygons as a special case: the regularity of uniform polygons follows from the same definition of uniform as applies to higher dimensions, combined with the limited repertoire of Flatland symmetries. George's definition is not wrong – it produces an equivalent set – but it's unnecessarily complicated. It is certainly worth mentioning that all uniform polygons are regular, but not as part of the definition of uniform.

Oops, hang on – there does need to be something about equal edges; a rectangle has a symmetry group transitive on the vertices. —Tamfang (talk) 06:43, 15 August 2008 (UTC)

Yes, regular faces is the restriction against general isogonal figures... Tom Ruen (talk) 18:19, 15 August 2008 (UTC)

The upshot is that I'd put the base of the inductive definition one step lower: vertex-transitivity and equal edges rather than vertex-transitivity and regular faces. —Tamfang (talk) 00:53, 22 August 2008 (UTC)

Right. Either way is okay with me, if you really like to rewrite it. Tom Ruen (talk) 02:06, 24 August 2008 (UTC)

The Uniform polyhedron article says A uniform polyhedron is a polyhedron which has regular polygons as faces and is transitive on its vertices (i.e. there is an isometry mapping any vertex onto any other)., so the regular face

I suppose I prefer the regular polygon face definition because it means something stronger than equal edges, even if regular faces can be deduced from the two requirements: isogonal figures and equal edges. There's redundancy in the regular polygonal definition, but it's good redundancy in my view. Tom Ruen (talk) 02:14, 24 August 2008 (UTC)

Stellation images

Tom, At least some of your imeages of icosahedral stellations have obsolete license info which needs updating <sigh>. Also, everything needed for The fifty nine icosahedra is now there, except for the remaining stellation images. Hoping you might be able to oblige in due course <grin>. -- Cheers, Steelpillow (Talk) 10:54, 17 August 2008 (UTC)

I just got back from a week vacation. I'll try to get some time to finish the diagrams, images (and fix the licensing). Tom Ruen (talk) 02:15, 24 August 2008 (UTC)

Math notation style corrections

I still keep coming across large numbers of things like

{p}x{q}

instead of

{p}×{q}

(italics for p and q, and a proper times symbol rather than an x). Or

(n-2)-dimensional

rather than

(n − 2)-dimensional

(italicized n, an actual minus sign instead of a stubby little hyphen, spaces before and after the minus sign; on the browsers I use the differences are very conspicuous).

You edit a lot of these polyhedron articles. Can you help bring them closer to the norms of Wikipedia:Manual of Style (mathematics)? Michael Hardy (talk) 15:16, 18 August 2008 (UTC)

Hmmmm... I have to admit style for me is not very important. I believe in standards and consistency, but I can't see myself going far out of my way for this (i.e. doing anything I can't type in my keyboard instantly). Sorry. Tom Ruen (talk) 02:05, 24 August 2008 (UTC)

Polychora vertex data

Hi, just wondering if you happen to have (or know where to get) data files containing the vertices of the uniform polychora? Recently I wrote a program for doing perspective projections of polychora into 3D with hidden-cell culling (which I believe is the best way of visually understanding these objects), and I'd like to test it on as many polychora as I can to see if it's something useful to add to wikipedia. If you're interested, I can upload a few of the animations I've made so far for your review. Thanks!—Tetracube (talk) 23:09, 19 August 2008 (UTC)

Stella (software) (4D) can generate them all, but only exports 3d projections. I have some data from my program. I put an example export at User:Tomruen/temp - truncated 16-cell, vertices, edges, and faces. Vertices are listed first (x,y,z,w). Then edges index vertices. Then faces index vertices, with the vertex count first. I never got around to reconstructing cells. Tell me if you can use this. Tom Ruen (talk) 02:00, 24 August 2008 (UTC)

Thanks, all I need are the vertices. I've figured out how to extract the complete face lattice from just the vertices with the help of Komei Fukuda's cdd/libcdd utilities. Right now, I have a script that compiles the various output files of cdd and libcdd's allfaces into a unified format that my program uses (which includes the full face lattice plus facet normals). I could probably generate some of the uniform polychora by hand simply by adding more bounding halfspaces to cdd's H-representation, and regenerating and recompiling the data.

On another note, if you're ever interested in full face lattice data, just let me know and I'll put it up somewhere.—Tetracube (talk) 16:38, 25 August 2008 (UTC)

On a related note, I've made a sample animation using the povray output generated by my polytope viewer program:

This is the bitruncated 24-cell projected into 3D using parallel projection. The cell nearest the 4D viewpoint has been highlighted, and edges and vertices are shown except for those lying on this cell (this is all configurable). The ridges are rendered transparently so that the inner structure of the projection can be seen, except for those lying on the highlighted cell (to reduce visual clutter). The rotation is only in 3D, and is mainly to show the structure of the 3D image more clearly.

What do you think, is this suitable to include in bitruncated 24-cell?—Tetracube (talk) 19:45, 25 August 2008 (UTC)

Looks great. I can give you some more uniform polychoron datasets, but not set up to easily generate them all. Well, specifically I can generate all but the snb 24-cell, and Grand Antiprism, given a vertex figure. You could probably do this too - just take the vertex figure as a set of vectors on a 3-sphere. Reflect the vertex figure across the hyperplane tangents to each vector, and recursively repeat until all vertices are created. WELL, that said, you do need the vertex figures, which I have the files somewhere. I could email them to you. Tom Ruen (talk) 23:58, 25 August 2008 (UTC)

Sure, it would be nice to have some data to start with. Also, I believe I've figured a way to construct the grand antiprism and the snub 24-cell from the 600-cell, by selectively deleting certain vertices and recomputing the convex hull. If this works, I'll let you know. :-)

Also, is there a widely-used file format for exchanging polytopes? Currently, my lattice computation program understands the cdd format ('cos that's what cddlib understands), but the format is not capable of representing the face lattice or storing facet normals (needed for projections), so I use a homebrew format for my projection program. If there is a widely-used polytope format, I'd like to implement import/export functions for it.—Tetracube (talk) 20:30, 27 August 2008 (UTC)

Stella 4D allows a "4OFF" import format (but doesn't export it). I can't find any definitions, but reference here at least.[4].

Example from Stella4D (Vertices listed, faces indexed by vertices, cells indexed by faces.)

#Tesseract
4OFF
# Vertices, Faces, Edges, Cells.  Edges is ignored and may be 0.
16 24 32 8

# Vertices
-0.50000000000000000 -0.50000000000000000 -0.50000000000000000 -0.50000000000000000
-0.50000000000000000 -0.50000000000000000 -0.50000000000000000  0.50000000000000000
-0.50000000000000000 -0.50000000000000000  0.50000000000000000 -0.50000000000000000
-0.50000000000000000 -0.50000000000000000  0.50000000000000000  0.50000000000000000
-0.50000000000000000  0.50000000000000000 -0.50000000000000000 -0.50000000000000000
-0.50000000000000000  0.50000000000000000 -0.50000000000000000  0.50000000000000000
-0.50000000000000000  0.50000000000000000  0.50000000000000000 -0.50000000000000000
-0.50000000000000000  0.50000000000000000  0.50000000000000000  0.50000000000000000
 0.50000000000000000 -0.50000000000000000 -0.50000000000000000 -0.50000000000000000
 0.50000000000000000 -0.50000000000000000 -0.50000000000000000  0.50000000000000000
 0.50000000000000000 -0.50000000000000000  0.50000000000000000 -0.50000000000000000
 0.50000000000000000 -0.50000000000000000  0.50000000000000000  0.50000000000000000
 0.50000000000000000  0.50000000000000000 -0.50000000000000000 -0.50000000000000000
 0.50000000000000000  0.50000000000000000 -0.50000000000000000  0.50000000000000000
 0.50000000000000000  0.50000000000000000  0.50000000000000000 -0.50000000000000000
 0.50000000000000000  0.50000000000000000  0.50000000000000000  0.50000000000000000

# Faces
4 0 2 3 1 	255 255 255
4 0 4 5 1 	255 255 255
4 0 4 6 2 	255 255 255
4 0 8 9 1 	255 255 255
4 0 8 10 2 	255 255 255
4 0 8 12 4 	255 255 255
4 4 6 7 5 	255 255 255
4 2 6 7 3 	255 255 255
4 1 5 7 3 	255 255 255
4 2 10 11 3 	255 255 255
4 1 9 11 3 	255 255 255
4 1 9 13 5 	255 255 255
4 8 10 11 9 	255 255 255
4 8 12 13 9 	255 255 255
4 8 12 14 10 	255 255 255
4 4 12 13 5 	255 255 255
4 4 12 14 6 	255 255 255
4 2 10 14 6 	255 255 255
4 12 14 15 13 	255 255 255
4 10 14 15 11 	255 255 255
4 9 13 15 11 	255 255 255
4 6 14 15 7 	255 255 255
4 5 13 15 7 	255 255 255
4 3 11 15 7 	255 255 255

# Cells
6 0 2 7 8 1 6 	255 0 0
6 0 4 9 10 3 12 	255 0 0
6 1 5 15 11 3 13 	255 0 0
6 2 5 16 17 4 14 	255 0 0
6 6 16 21 22 15 18 	255 0 0
6 7 17 21 23 9 19 	255 0 0
6 8 11 22 23 10 20 	255 0 0
6 12 14 19 20 13 18 	255 0 0

I've not seen any other examples. Obj could trivially be extended for 4D, adding 4th coordinate and cells by indexed faces.

Tom Ruen (talk) 00:31, 28 August 2008 (UTC)

OH, if you want to email me at [5], I can send you the Uniform polychora vertex figure data (zipped and stored in OFF format). Tom Ruen (talk) 00:34, 28 August 2008 (UTC)

Hmm, what do the columns of 255 signify? I assume "255 255 255" must mean something specific to faces, and "255 0 0" something specific to cells. In my homebrew format, I store the face lattice as vertex sets (so that it's easy to test if an n-face is contained by an m-face: it's precisely when the first vertex set is a subset of the second). It's not too difficult to convert to/from this. (The main reason for using vertex sets is for visibility clipping: it's easy to compute which vertices are visible from a given 4D viewpoint, and once we have that, we simply filter all the other elements by whether their vertex sets are subsets of the set of visible vertices.)

But is there no widely-used generic format for n-dimensions? I can see how Obj, or OFF and 4OFF, may be generalized to n dimensions, but it doesn't sound like the software would readily understand it.—Tetracube (talk) 17:23, 28 August 2008 (UTC)

Sorry for not explaining. The 255,0's are Red-green-blue color levels for the faces and cells. They can be ignored. I think Stella keeps the face colors for OFF, and cell color for 4OFF. And yes, extending an existing format is only useful if you're the programmer using it! I have a java application for viewing 3D surfaces by vertices and faces, reading/writing (a subset) various formats, DXF, OFF, OBJ, VRML, RAW. My 4D polytope program exports 3D projection data, or my variation on 4OFF like I shared with you. Tom Ruen (talk) 18:09, 28 August 2008 (UTC)

Ah, I see. So it shouldn't matter if I omit the color levels? Also, IMHO a file format really is most important for sharing between applications (or users), so I'd like to reuse an existing, commonly-accepted format if there is one. Looks like there isn't, unfortunately. I'm tempted to invent my own, but then if nobody else (or only a small minority) uses it, it serves no purpose either.

On a side note, have you replied to my email by any chance? My spamfilter appears to be malfunctioning, so apologies if it got lost. Please let me know if this is the case, and I'll try to fix it.—Tetracube (talk) 23:10, 28 August 2008 (UTC)

Sorry, I didn't get your email. I looked in my spam folders. Try my yahoo.com address, at tomruen. I just get worried about publishing my address online for uncertain risk of spam webspiders. Tom Ruen (talk) 17:49, 29 August 2008 (UTC)

Tilings

Tom, I see that you have put up a lot of articles on higher-dimensional tilings using Tetra- Penta- and Hexacombs nomenclature. Has this ever been properly referenced? AFAIK George Olshevsky's naming of specific dimensionalities has yet to achieve wide acceptance. I am concerned that the present article titles appear to constitute the dreaded Original research, and if so then we ought to re-name them.

Also, what about the individual names? Might these be equally OR? And looking at the shortness of the average article, I wonder if it would be better to merge them into fewer but more comprehensive articles, for example Uniform tilings of 4 space would accommodate most if not all "tetracombs".

Coxeter used the term honeycomb, while tiling and tessellation are common alternatives which also include plane fillings. In fact the whole set of these pages needs rationalising and reorganising. I'd suggest "tiling" as the shortest, and hang all the others off a new/merged Tiling (geometry) article. I notice also that the main category for all these is Category:Tiling.

Thoughts? -- Cheers, Steelpillow (Talk) 15:07, 2 September 2008 (UTC)

I think there's only 3 "tetracombs" listed, at List_of_regular_polytopes#Tessellations with individual articles, and a few linked that have no articles. There's also articles like E8 lattice. I definitely prefer "honeycomb" for 3D tessellations, and "tiling" for 2D since both usages match their origins. What 4D or higher tessellations SHOULD be called, I don't know. Coxeter uses "honeycomb" as a general dimensional term, so that's fine with me. It's just a little confusing to name things identically in different dimensions, which goes back to George O's approach. I suppose n-polytope means an n-dimensional polytope, then n-honeycomb means an n-dimensional honeycomb, BUT I've not seen this used anywhere. On a polytope level, there's also ambiguous use of "prism" by dimensions, and so a "polygonal prism" can mean like {p}x{}, and a polyhedral prism can mean {p,q}x{}. So anyway, we could use "polygonal honeycomb" = "polygonal tiling" = "tiling", AND "polyhedral honeycomb" = "3-honeycomb", and "polychoral honeycomb" = "4-honeycomb". AND so for specific forms it is always clear anyway: Tesseractic tetracomb = Tesseractic honeycomb. WELL, so all I'm saying is replace "tetracomb" with "honeycomb" I guess. OH, I don't like tessellation since it seems more general, may imply any repeating pattern, not just edge-to-edge polytopic forms.

On Uniform tilings of 4 space, I agree we're in trouble with the current Convex uniform honeycomb for 3-honeycombs, "convex" implying convex cells and vertex figures. And Uniform tiling now for 2-honeycombs. I suppose I do like Convex uniform 4-honeycomb for the next level, but accept it isn't a standard. Tom Ruen (talk) 15:28, 2 September 2008 (UTC)

Sadly, what we prefer and what Wikipedia policy dictates are not necessarily the same thing. We cannot adopt terms which are not in the main stream. A quick google reveals "tiling" + 'n dimensional'" or "tiling" + 'n dimensions'" to be more popular than either of the honeycomb or tessellation equivalents. However "n-dimensional tiling", "tiling in n dimensions" and "tiling of n-space" all have few hits (and the others fewer still). Also, "tiling" embraces the 2D and 1D cases, which "honeycomb" does not. "n-tiling" is used with a different meaning altogether. Thinking of Grunbaum (& Shephard?)'s Uniform tilings of 3-space, I would suggest we go with "Tilings of n-space" unless/until the body of more recent literature turns up something better. -- Cheers, Steelpillow (Talk) 20:33, 2 September 2008 (UTC)

Coxeter talks of "3-dimensional honeycomb" and "n-dimensional honeycomb". It looks like Coxeter says "Tessellation" rather than "tiling" for the plane, like he says a {3,6} tessellation' as well as a "{4,3} spherical tessellation". I see really George's tetracomb approach is unnecessary since honeycombs are named by their facets, so the dimension is already defined. Tom Ruen (talk) 18:30, 4 September 2008 (UTC)

I think I've removed all the tetracomb, pentacomb namings, into honeycombs. Tom Ruen (talk) 20:03, 4 September 2008 (UTC)

Some polychora images for review

Hi Tom Ruen, I've put up a little gallery of various polychora renderings from my polytope program here: User:Tetracube/Gallery of polychora. What do you think? Can we put some of them on the main polychora pages? Thanks!

P.S. These are mainly thumbnail size because they are just sample renders; if necessary I can do other enhancements such as rendering (some subset or all of) edges or vertices, hiding some ridges, etc..—Tetracube (talk) 00:49, 28 September 2008 (UTC)

They look good, a bit hard to see them at small size. It's great to get more transparent images. Stella4D doesn't do transparency. I assume you're "doing it right" - sorting faces by depth before rendering. I know from experience a simple implementation with OpenGL leads to artifacts based on drawing order. Tom Ruen (talk) 02:56, 28 September 2008 (UTC)

These images are raytraced by POVray, so depth sorting isn't an issue (it's already taken care of by definition of raytracing). However, I do plan to write a GL renderer backend for it eventually; so thanks for the warning.

What do you think about including these images in the polychoron articles, though? Are they suitable as-is (well, maybe at higher resolution), or should I add some enhancements, like render some edges/vertices, hide some ridges, etc.?—Tetracube (talk) 17:24, 29 September 2008 (UTC)

Please include as many as you like, especially if you're willing to write descriptions of each. Ideally every image exists to illustrate something specific, including comparative images between forms. Like for the uniform polychoron page with small table images, I started trying to add systematic images between the truncated forms in each family, but didn't finish. Anyway, please upload some higher resolution versions and add to the pages, even Convex regular 4-polytope could use some improvements for comparison - VEFC-centered orthogonal projections, and your transparency plus selected central elements seems a great addition if you want to add more rows for each orientation. I look forward to seeing whatever you can do. (Well, my only thoughts, perhaps ALL images should have maybe "thin" edge lines everywhere, even if you show wider lines to show certain cells too, just a quick thought from the hard-to-see small images. It's really an art I guess to see how much you can show without getting overwhelming or confusing.) Tom Ruen (talk) 17:32, 29 September 2008 (UTC)

Currently, my program only renders edges one way, but I'm working on extending it so that I can apply arbitrary textures (and other properties) to them. Anyway, with what limitations there currently are, I can still make some images that I think are quite nice; I added multilayer renders to 120-cell and 600-cell. Hope you like them. I'll add more as time permits.—Tetracube (talk) 19:37, 29 September 2008 (UTC)

A good start. I look forward to some higher resolution images. :) Tom Ruen (talk) 21:40, 29 September 2008 (UTC)

How high a resolution are you looking for? I've added quite a number of new images to 24-cell and snub 24-cell (I figured out how to construct the latter from the 600-cell: it's not very hard since the coordinates I have for the 600-cell can be trivially filtered to obtain the vertices of the snub 24-cell), all at 320x240. I'm not so sure about uploading large numbers of images at high resolution, though. Would 800x600 be enough?—Tetracube (talk) 17:01, 6 October 2008 (UTC)

P.S. I made a sequence of images comparing projections of a cube vs. projections of the tesseract, and I'm wondering how to incorporate it into the tesseract article. Any suggestions? The draft is here: User:Tetracube/Comparison of cube and tesseract —Tetracube (talk) 23:34, 6 October 2008 (UTC)

Minneapolis Meetups

Town Hall Brewery
maps.google.com
1430 Washington Ave S
Minneapolis, MN 55454
(612) 339-8696
October 11, 2008
Saturday at 12:00 noon (midday)
Meetup RSVP

Muddy Waters
maps.google.com
2401 Lyndale Ave S
Minneapolis, MN 55405
(612) 872-2232
October 10, 2008
Friday at 10:00 PM (at night)
Alternate meetup RSVP

Hope you can make it. Feel free to pass along these invitations. -SusanLesch (talk) 17:55, 8 October 2008 (UTC)

images on the commons

which good images dear Tomruen --Mardetanha ^talk 19:58, 5 October 2008 (UTC)

I see, you're so lazy, you can't even look up a history! Try these two - you deleted them in the same hour and minute! Tom Ruen (talk) 21:21, 5 October 2008 (UTC)

http://commons.wikimedia.org/wiki/Image:E8_graph.svg

http://commons.wikimedia.org/wiki/Image:Johnson_solid_37_net.png

person who uploads image should fulfill all requested licensing and sourcing material.anyway you have uploaded image and the image was deleted because of inadequate information.--Mardetanha ^talk 09:36, 6 October 2008 (UTC)

That doesn't tell me anything. You should contact people who upload images if there's a problem. How do you expect anyone to learn when you just delete and give no feedback, no warning, nothing at all!!!

SO WHO ARE YOU, and why do you consider it your responsibility to delete images like this?! Tom Ruen (talk) 02:34, 7 October 2008 (UTC)

Sorry dear Tomruen.And please accept my sincere apology about my delay in answering.in commons when someone marks image for deletion normally we give the user information about that.i think in your issue some miss fortunate happened.so anyway i am at your service anytime.just be advised i myself as admin just delete the image after 8 days.--Mardetanha ^talk 00:37, 9 October 2008 (UTC)

Image:CD_9-5.png listed for deletion

An image or media file that you uploaded or altered, Image:CD_9-5.png, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. O sama K^{Reply? on my talk page, please} 03:19, 18 October 2008 (UTC)

Proposed deletion

This edit seems to suggest that it is not established Wikipedia policy that that is not grounds for deletion. Lists and categories coexist. Categories are in many ways far inferior to lists, and in particular, see the AfD discussion for list of Fourier analysis topics. Michael Hardy (talk) 01:10, 25 October 2008 (UTC)

Sorry, I picked the wrong template on first attempt, changed it immediately. I wrote my reasons for deletion. Perhaps someone will make it more useful than now? I don't know what would make it more useful. Tom Ruen (talk) 01:53, 25 October 2008 (UTC)

Cupolas (polychora)

Hello Tomruen!

I saw you made most of Schlegel diagrams of the uniform polychora with Stella 4D. I need your help for the Schlegel diagrams of the 4-cupolas (see cupola). The cupolas form a family of polytopes, like prisms or pyramids. Overlapped, they composed the uniform polytope obtained by the expansion of the regular polytopes (for polyhedra see cuboctahedron, rhombicuboctahedron and rhombicosidodecahedron). I worked on this and I think I've found all of the 4-cupolas. Now I need you to draw these cupolas: could you help me? If you agree I'll give you more informations.

Thank you.

Padex (talk) 14:34, 15 November 2008 (UTC)

PS: I'm French so please excuse-me for all mistakes...

Edit: I just saw that you made all nets of Johnson solids... so you know cupolas =D.

Padex (talk) 17:00, 15 November 2008 (UTC)

Hi Padex. I understand what you're suggesting, although I've not seen these referenced anywhere. It would be cool to show them. I suppose they're a part of a (finite?) family of Johnson polychorons, ALTHOUGH not exactly, since Johnson solids have regular faces, while these have semiregular cells. (An expanded regular n-gon is a regular 2n-gon, but an expanded regular {p,q}-hedron is merely semiregular.) Still interesting to imagine. I don't have time right now to really help. I use a program called Stella4D for most of the images I've uploaded. I think it can import 4D coordinates of polychora using a 4D OFF format, but it was unstable in cases I tried, tolerance issues.

These figures are simple enough, maybe don't need something really complicated. Like my transparent image at Cuboctahedral_prism - Image:Cuboctahedral_hyperprism_Schlegel.png, these can be represented by two nested polyhedra connected by edges.

I guess the cells are {p,q}, t0,3{p,q}, n-gonal prisms, and n-sided pyramids. Well, again, shows these are not even semiregular, since n-sided pyramids are only regular for triangles.

How about starting with an element table on a user page, like User:Padex/hypercupola? Tom Ruen (talk) 22:52, 15 November 2008 (UTC)

Good idea! I will start an element table, which describe all the cupolas I've found. After I'll try to calculate the 4D coordinates.

I don't know how Norman Johnson defines the Johnson polychora, but I'm sure these are some. When we will have finished, I think we can put them on the cupolas page, or we can create an other, I don't know yet.

You're right, there are {p,q}, prisms and pyramids, but I guess you would say t0,2{p,q}, cause it's not possible to runcinate a polyhedron, is it? Padex (talk) 11:12, 16 November 2008 (UTC)

I'm in occasional contact with Norman Johnson and have never known him to show any interest in nonuniform polychora, so define them how you like. ;) —Tamfang (talk) 04:33, 18 November 2008 (UTC)

In generalizing from polyhedra to polychora, there are two approaches: (1) generalize the characteristic property of the faces (e.g., regularity) to cells (the polychora must have regular cells); or (2) generalize the characteristic property of the polyhedron itself (e.g., it is uniform) to cells (the polychora has uniform cells). The former approach, as applied to uniform polyhedra, give us the 3 semiregular polychora (cells must be Platonic solids); the latter approach give us the full spectrum of uniform polychora (including unusual ones such as the grand antiprism and the series of duoprisms). When generalizing the Johnson solids, one could either generalize by way of polychora with Platonic solid cells, or by way of allowing Johnson solids themselves to be cells.—Tetracube (talk) 04:45, 18 November 2008 (UTC)

P.S. If you have 4D coordinates for your polychora, I can render them with my polytope projection program. It performs perspective/parallel projection at a distance (which I find more intuitive, unlike Schlegel diagrams) with two distinct viewpoints for 4D->3D and 3D->2D projections, and can cull back-facets if desired. Just drop me a note.—Tetracube (talk) 04:50, 18 November 2008 (UTC)

I'm glad my talk page is helpful. I mentioned idea of "Johnson polychora" made of regular polychora, but these (hypercupula) fail any useful extention. Still they're a pretty class to add, a useful start that goes beyond uniform polychora, although no tables with hyperpyramids either. I hope Tetracube could render these! :) Tom Ruen (talk) 05:09, 18 November 2008 (UTC)

I put the cartesian coordinates of the cubic and the octahedral cupolas. Thank you Tetracube for helping me, but I'm sorry I prefer Schlegel diagrams. However, it may be the same with your method, because cupolas are simple. I just hope I made no mistake in my calculation.

Really Tamfang? Norman Johnson has never been interested by a generalisation of his own solids? So am I the first? ^^

Padex (talk) 18:19, 19 November 2008 (UTC)

I said I have never known him to show interest. That's a limited sample. —Tamfang (talk) 07:51, 20 November 2008 (UTC)

OK, here are two renders of the cubic cupola:

The first is a perspective projection looking from <0,0,0,-5> at the top cubic cell, shown here in red. This is pretty close to the Schlegel diagram, I believe; you can see the rhombicuboctahedral cell on the outer envelope of the projection. The second is a perspective projection looking from <4,0,0,-1>, a sort of "side-view", if you will. Here, you can see the top cell (red) and the bottom cell (blue) foreshortened.

Looking at these images, I'm not sure if the coordinates are right; the rhombicuboctahedron appears to have elongated rectangular faces surrounding the axial square faces. Did I read the coordinates wrongly, or is the rhombicuboctahedron not intended to be uniform?

Anyway, hope y'all like these images. :-) —Tetracube (talk) 21:40, 19 November 2008 (UTC)

Oh! I'm sorry I had the good results but I made a mistake when I decided to simplify the coordinates by using τ : the value was false. Sorry. It's the same for the octahedral cupola...

Thank you anyway! Padex (talk) 16:10, 20 November 2008 (UTC)

OK, I've replaced the images with the correct coordinates. I assume

\tau ={\sqrt {2}}/2

is correct, right? It does look uniform to me now.—Tetracube (talk) 18:59, 20 November 2008 (UTC)

I don't know the context here, but τ usually means the golden ratio. (I prefer it to φ because I often have occasion to use the latter for colatitude.) —Tamfang (talk) 00:27, 21 November 2008 (UTC)

Made another update to the first image; the previous one was clipped slightly 'cos the viewpoint was too close to the polytope. Should be good now.—Tetracube (talk) 19:06, 20 November 2008 (UTC)

More images for your viewing pleasure: this time it's the octahedral cupola.

The first is a perspective projection centered on the octahedral top cell, viewed 5 units away, which should be pretty close to the Schlegel diagram. You can see quite an interesting structure here, which shows how the octahedron's elements are mapped to the rhombicuboctahedron! The second is a side-view level with the bottom cell (so it appears flat). One square pyramid is highlighted in yellow, and hidden cells are culled for clarity.—Tetracube (talk) 20:23, 20 November 2008 (UTC)

Thank you. I added the tetrahedral cupola. Padex (talk) 19:34, 22 November 2008 (UTC)

Very nice! A Cubic cupola seems a consistent name, like square cupola. I think technically there could be multiple types of such figures. We're talking an Expansion (geometry) operation here which is dimensionally generalized, but could imagine a truncated cube-cube pair (truncation is expansion operation on polygons). And looking more, I see we could have at least five categorical forms?!

...and three more if you add bitruncated, bicantellated, and dualed. Well, I've not thought hard enough to "see" all the connecting cells, but intution suggests they're all somethin'!

Tom Ruen (talk) 02:48, 21 November 2008 (UTC)

P.S. I've not looked. I wonder if all of these (or any) can be made with all equal edge lengths, and all regular polygon faces? Tom Ruen (talk) 02:53, 21 November 2008 (UTC)

I don't think so. For example the dual of dodecahedron is the icosahedron, and icosahedral cupola isn't "regular" (i.e. with "all equal edge lenghts and all regular polygon faces). With my idea of cupolas there are only four, but there are other families of polychora. You wrote the "Cubic truncated cupola": you can see it in the Runcitruncated tesseract, but it's not a real cupola, I think (however, as Tetracube said, there are several way to generalize). Thank you again Tetracube! Padex (talk) 18:27, 21 November 2008 (UTC)

I can see there's a "height" limitation on equal-edges - like there's no hexagonal cupula because the height goes to zero, as shown in the small rhombitrihexagonal tiling. So perhaps some forms like icosahedral cupola' (Icosahedron with the expanded-form, rhombicosidodecahedron) can't be connected in 4-space with the same edge lengths. Have you checked which ones exist? Tom Ruen (talk) 21:46, 21 November 2008 (UTC)

Not yet ^^. I have to find the coordinates of the Dodecahedral cupola before, then create a page with the projections of Tetracube, and the Schlegel Diagram (to have all polychora with the same software). After I'll study the others, but sorry not until I've finished that. Padex (talk) 21:10, 22 November 2008 (UTC)

I've found a document what I think cheks all type of cupolas, here: [www.orchidpalms.com/polyhedra/segmentochora/artConvSeg_7.pdf]. I'm definitively not the first ;). What about in 5D? =D Padex (talk) 18:29, 23 November 2008 (UTC)

Uniform polytera

Hi Tom Ruen, I've found a way to generate the Cartesian coordinates of all uniform polytopes derived by truncations of the n-cube/n-cross. I've started User:Tetracube/Uniform_polytera to try to map these coordinates in 5D to known uniform polytera; do you happen to know any sources for verifying this? Thanks!—Tetracube (talk) 01:23, 22 November 2008 (UTC)

Sorry, I only have a source with element counts, given at User:Tomruen/uniform_polyteron. Tom Ruen (talk) 01:28, 22 November 2008 (UTC)

Incidentally, my primary source is copied online at: [6]

Actually, what you have on User:Tomruen/uniform_polyteron is sufficient. The derivation method I use makes it easy to identify a generated polytope once the axial facets (those lying in hyperplanes parallel to the n-cube's facets) are known. I think we should merge the info from both pages; what do you think?—Tetracube (talk) 16:28, 22 November 2008 (UTC)

There's also 5-polytope which is a start. I planned to move much to uniform polyteron if I got my facet table elements completed. Anyway, I'm okay if you want to edit on User:Tomruen/uniform_polyteron. I tend to think best to avoid coordinate information on a summary page since can only be given for a subset of uninform polyteron figures. Anyway, I'm open whatever you want to try. Maybe your work will inspire me to finish my tables - basically just reading the CD graphs, extracting polychora, and connecting up links and images. Tom Ruen (talk) 19:15, 22 November 2008 (UTC)

Okay I moved uniform content from 5-polytope to uniform polyteron (which had been a redirect), not great, but a start. Tom Ruen (talk) 19:53, 22 November 2008 (UTC)

For extracting polychoral cells, I found a correspondence between (n+1)-hypercubic truncates and n-simplicial truncates which makes it very easy to determine which simplicial truncates serve as corner facets in an (n+1)-hypercubic truncate. This also gives Cartesian coordinates for the simplicial truncates, although this is in (n+1)-space and not origin-centered; some massaging is needed to express it in n-space.—Tetracube (talk) 01:44, 23 November 2008 (UTC)

Jessen's icosahedron

Discussion section moved to: Tom Ruen (talk) 00:59, 24 November 2008 (UTC)

Talk:Jessen's icosahedron

Sunrise animation

Hi Tom
I've included the sunrise animation that you created (uploaded by "Saperaud") in my video
The Storm
Many thanks
Dwsolo (talk) 20:51, 8 December 2008 (UTC)

Number of vertices on cantitruncated 24-cell

Hi Tom Ruen, I computed the Cartesian coordinates for the cantitruncated 24-cell and checked the resulting element counts after running a convex hull algorithm, and I get matching numbers and types for cells, faces, and edges, but I have 768 vertices whereas the current uniform polychoron pages all have 576. I looked at George Olshevsky's archived pages, and he seems to have 576 vertices as well. I don't understand the discrepancy; did he make a mistake with that number? I've checked the output of my polytope viewer, and I can't see how one can possibly reduce the number of vertices and still get the same numbers/types of cells, faces, and edges. I'm not sure if you (or whoever rendered that Schlegel diagram) still have the coordinates handy; could you check if the number of vertices is right?? Thanks!—Tetracube (talk) 01:29, 10 December 2008 (UTC)

Actually, nevermind that. I just realized that 192 vertices in the convex hull are redundant (not connected to any cells). So 576 is right. Mea culpa.—Tetracube (talk) 01:34, 10 December 2008 (UTC)

I'll bite. How can the convex hull of X have vertices that are not vertices of X? —Tamfang (talk) 08:14, 12 December 2008 (UTC)

I meant that some input vertices were redundant (not vertices of the hull). Oops.—Tetracube (talk) 19:19, 12 December 2008 (UTC)

Dual polygon: new page?

Hi Tom,

The topic of Dual polygons is properly not a sub-subject of regular polygons (other polygons have duals too!), so I’m planning on starting a separate article. I notice you have an interest in the topic; does this sound ok?

Nils von Barth (nbarth) (talk) 19:54, 10 December 2008 (UTC)

Glad for whatever you can add. Duality is a fuzzy subject, topologically every polygon is self-dual. Geometrically every regular polygon is self-dual. Some of the polyhedron content for duality by inversion can be useful for polygons too, but I've seen no sources that do this. The Dorman Luke construction diagram example shows its relation in polyhedra. A dual polyhedron has faces which are dual polygons of the vertex figure, so a rectangular vertex figure becomes a rhombic faced-dual polyhedron. Tom Ruen (talk) 22:17, 10 December 2008 (UTC)

I’ve made a start (at Dual polygon) – hope it looks ok, and feel free to jump in!

Nils von Barth (nbarth) (talk) 00:15, 11 December 2008 (UTC)

File:Lunar libration with phase Oct 2007.gif

Hello, this image is great... but it is also large. Would you be able to create a much smaller version of this sequence for use on the Moon article; as this version was bogging down the Moon article. (I have removed it for now) - Roy Boy 03:11, 16 December 2008 (UTC)

Disregard the above, I used the File:Lunar libration with phase2.gif for the article. - Roy Boy 05:08, 16 December 2008 (UTC)

NOTE: You can resize with Wiki px size code:

. Tom Ruen (talk) 16:29, 16 December 2008 (UTC)

Polychoron coordinates

Hi, just thought you probably missed my reply on Talk:Cantitruncated 5-cell in the midst of other Wiki goings-on. How do you feel about replacing the current huge list of coordinates with simple coordinates in 5-space instead, along with a transformation that will map them to 4-space?—Tetracube (talk) 21:29, 19 December 2008 (UTC)

Coloring scheme for polychoron tables

Hi Tom Ruen, I see that you have reverted some color changes by an IP address user to a few polychoron articles, and I have done the same as they seem quite arbitrary. However, I have initiated dialogue with the person concerned, and it seems that he is at least willing to discuss this. We can use my talk page for discussion. Your input would be appreciated.—Tetracube (talk) 17:19, 22 December 2008 (UTC)

Image copyright problem with File:Quarter cubic honeycomb family verf.png

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