User talk:Tetracube/Archive 1

Thanks for the complements on the animated 24-cell. I just finished the 16-cell, and I'm working on the 5-cell now. I would love to tackle the 120 and 600, but I don't think I can build them vertex by vertex like I did for the others without going insane. Is there any algorithm that can generate a list of vertices and connecting edges for these shapes?

Here's the 120-cell VEF data - pretty clear format I hope User:Tomruen/120celldata. Tom Ruen 22:52, 20 February 2007 (UTC)

Thanks, that looks like exactly what I need. Now to bury myself in the mel documentation :) JasonHise 04:15, 21 February 2007 (UTC)

You built the 24-cell vertex-by-vertex?? Wow... and I thought I was the only one crazy enough to hand-code the face lattice of the 24-cell. :-) But yeah, for the 120-cell and 600-cell, you don't wanna be doing this by hand. 600 vertices and 1200 edges will do some serious injury to your wrists. I did write some Perl scripts for generating n-dimensional simplices, crosses, and cubes (full face lattice), although they are in a peculiar format I use for an experimental program I'm writing. I have a script for generating the 24-cell, but none for the 120-cell or 600-cell yet.

Oh, and BTW, are you planning on doing animations of the uniform polychora as well? I'm dying to see the bitruncated 24-cell in action. (Mainly to confirm whether it looks like what I see in my mind's eye.)—Tetracube 04:49, 22 February 2007 (UTC)

I figured out that mel scripting isn't powerful enough to handle the data structures I need for object construction, so I am currently planning to write a maya plugin capable of loading files in the VEF format you showed me to generate complete animated scenes automatically. This means that when it is done, I should be able to generate any 4D figure that I can find a VEF file for. Including the bitruncated 24-cell if you have it. — JasonHise 06:14, 22 February 2007 (UTC)

I can generate VEF data for all uniform polychora with reflection symmetry from vertex figure data, which I have. Maybe only the grand antiprism is outside my list? So anyway, just ask when you're ready. Tom Ruen 07:19, 22 February 2007 (UTC)

Hey, thanks a million for this! --Tony (Talk), Vandalism Ninja 23:13, 16 February 2006 (UTC)

Hi, Tetracube, I see we both use Linux (go Tux!), share an interest in polytopes (Branko Grünbaum was on my thesis committee), and also share concerns about the claims made in Bios theory. I just wanted to let you know that in Talk:Bios theory I have enumerated almost a dozen serious problems with just the first paragraph. I have also listed evidence of a troubling conflict of interest on the part of User:Lakinekaki. Even worse, I have listed evidence of an apparent hidden agenda on the part of the organization which appears not only to employ Lakinekaki but also to be apparently the sole sponsor of "research" on "bios theory" (sic). What to do? ---CH 06:53, 12 May 2006 (UTC)

As a major contributor to the Polychoron articles, I need to ask you: Can you supply a reference to the term being used in a peer-reviewed journal? If not, it's got to go. 16:38, 14 July 2006 (UTC)

See Talk:Polychoron. The term is coined by Norman Johnson (the mathematician after whom the Johnson solids are named). According to Jonathan Bowers, Norman is currently writing a book on this subject. If this is not notable enough, then we might as well remove all the math articles. Personally, I couldn't care less whether or not the term itself is used in these articles, but I submit that it would make the wikipedia entries so much less readable if we are forced to use the cumbersome "4-dimensional polytope" every time we want to talk about these things. As for the notability of the polychora themselves, the convex uniform polychora have been known at least since the 19th century (IIRC—it may well be earlier, since the regular 4-polytopes have been known for a lot longer than that). I'll have to look up the reference for this—there is actually a paper that describes these things.—Tetracube 16:47, 22 July 2006 (UTC)

Acknowledged. I may comment further, there &mdash and, I really was only asking about the name. Uniform polytopes seem sufficiently notable to me, (although self-intersecting polytopes, in general, need a better definition) even if I cannot find a reference at the moment. I understand that 4-space has unique properties in regard non-prismatic regular polytopes. — Arthur Rubin | (talk) 19:02, 22 July 2006 (UTC)

I'm just curious; why must the 2-facets (faces?) be regular. One could construct the following recursive definition:

If n ≥ 2, then an n-dimensional polytope is said to be uniform if

1. All facets of dimension 2 through n-1 are uniform, and
2. For any two vertices, there is an isometry mapping one to the other.

(0- and 1- polytopes are trivially uniform, under almost any definition, so I'm restricting the definition to dimensions 2 and higher.)

The uniform polygons would then still have equal angles at each vertex, but might have two different (alternating) edge lengths.

It seems to me to be more geometrically intrinsic than the definition used. — Arthur Rubin | (talk) 22:03, 8 August 2006 (UTC)

I've actually thought about this before, too. In fact, I'd be interested to see the consequences of allowing non-regular 2-faces on polytopes: there'd be a lot more variety! However, that is not the current understanding of the term "uniform", at least as it applies to 3D. Otherwise, you'd have an uncountable number of, say, truncated tetrahedra (truncate the vertices of the tetrahedron by some arbitrary amount up to, but not including, 1/2 edge length). Many of the current Archimedean polyhedra would have infinitely many variants. Allowing 3-faces to be non-regular doesn't quite have the same effect as long as they are still Archimedean, since there are only a countable number of Archimedean polyhedra. (Not saying this is good or bad, but it does give us a lot of "redundant" polytopes that are almost the same.)

Now, as far as it relates to 4D polytopes, I suppose you could argue that allowing Archimedean cells seems rather arbitrary, and maybe we should stick with regular cells, in which case we get the semiregular 4-polytopes, of which there are only 3 (assuming convexity, of course). So it appears that allowing Archimedean cells makes for a much more interesting set of "uniform" polytopes, without making the possibilities too unbounded. I have no experience with 5D polytopes or above, so I don't know how the situation pans out there, but I suspect the situation would be more straightforward.—Tetracube 03:39, 9 August 2006 (UTC)

Well, thinking about it further, I can understand the reason for the definition, as any n-"box" (rectangular parallelepiped, hypercuboid) is uniform under my definition. For polyhedra, "clearly" an arbitrary truncation or cantellation of a regular polyhedron is "uniform". Still, it would be interesting to see if a further analysis could be done with this definition.

The new faces for the truncated {p,q} have each vertex becoming a regular q-gon and each face becoming a uniform 2p-gon.

The new faces for the cantellated {p,q} have each vertex becoming a regular q-gon, each edge become a rectangle (uniform 4-gon), and each face remaining a regular p-gon.

So there are at least those 10 1-dimensionally infinite families, and the 2-dimensionally infinite family of cuboids. — Arthur Rubin | (talk) 02:15, 11 August 2006 (UTC)

These infinite families are topologically identical to the archetypical Archimedeans that we have under the current definition. I don't find that quite as interesting... unless having unequal edge lengths can somehow give rise to (topologically) new polytopes that are excluded by enforcing equal edge lengths. I'd love to know if this is actually possible.

On another note, I'm quite interested in polytopes that have congruent facets but with no other constraints on the shape of the facets (except perhaps convexity). Catalan solids would fall under this category. (Has anybody studied 4D Catalans yet?) In 4D, interestingly enough, there are two non-regular, non-Catalan polychora that fall under this definition: the bitruncated 24-cell and the bitruncated 5-cell, which happen to also be uniform (under the existing definition). I'm curious to know if there are any non-uniform, non-Catalan examples of such polytopes.—Tetracube 05:10, 11 August 2006 (UTC)

The symmetry groups may depend on the precise edge lengths; for example, n-boxes have a symmetry group isomorphic to (Z₂)ⁿ Wr G, where G is the permutation group acting on the n dimensions which preserve the corresponding edge length, so the classification by permutation group becomes difficult.

But ... for (convex, anyway) uniform polyhedra, the vertex configuration must still have the same properties, as the angle defect is not affected by whether the polygons are regular or "uniform", and the topological requirements (in p.q.r(. ...), if q is odd, then p=r) still holds. Now, when that maps up to 4 dimensions, more complex combinations might be possible. — Arthur Rubin | (talk) 19:06, 11 August 2006 (UTC)

Hmm, I'm not sure I see why it might be different in 4D. As far as I can tell, the angle defect is still unaffected in 4D, so putting the polyhedra together isn't going to produce anything new. I may be missing something obvious, of course.—Tetracube 22:49, 11 August 2006 (UTC)

Hi Tetracube,

User:RobertAustin asked me to make a user box template for people who like polyhedra. You can add it to your main user page if you like it. You can see others who use it at (Special:Whatlinkshere/Template:User_Polyhedron). Tom Ruen 05:53, 7 January 2007 (UTC) ADD

This user is interested in polyhedra.

Cool, thanks.—Tetracube 03:42, 25 January 2007 (UTC)

Hey Tetracube! I'm on wikibreak for a week, but thought I'd ask your opinion. Check out images at [1] for possible candidates to replace uniform polychora images with a consistent set. They're from the new Stella (software) beta prerelease. Still trying to evaluate what's best but these orthogonal projections with solid cells are interesting, and useful, including the Schläfli-Hess polychoron. I also uploaded some new images for the duoprisms. AND I can make vertex figures and nets for all! Hardest thing is to make easy consistent coloring between, but can be done with patience. Also getting identical projection orientations takes some work. Anyway, thought I'd ask if you'd approve simpler orthogonal images. (OH, there is no "4D export" now, although I'm trying to encourage the developer to add one. He does have a 4D import, extending OFF format but including 4 vertex coordinates and listing cells by indced faces.) Tom Ruen 14:53, 25 February 2007 (UTC)

Can I ask how you got that pattern? --M1ss1ontomars2k4 (talk) 08:13, 12 December 2007 (UTC)

By painstakingly permuting the corner pieces into place. :-) Using the corner piece permute algorithm, of course. It is also possible to "solve" a scrambled Megaminx into that state, by aligning the edge pieces with the face centers, but rotating the first corner in the "wrong" orientation, and then using that as your reference for all subsequent corners as you solve it. But this is more confusing than simply starting from the solved state and permuting the corners.

For the 12-color Megaminx, there are two distinct types of stars, one where the corners are "rotated" 60 or 120 degrees relative to the rest of the puzzle, and another where they are "upside-down". The 6-color Megaminx only has the first type; the second type is a 10-star pattern because opposite faces are the same color in the 6-color Megaminx. You can obtain the first type by doing a random corner permutation, then permuting one of the corners back into place but with a "wrong" twist, and then using it as your reference for orienting the rest of the corners.—Tetracube (talk) 13:42, 15 December 2007 (UTC)

Just saw those nice pictures on the fourth dimension page and your gallery is great. I tried something a while ago on viewing tesseracts but without colouring the cubes and with much bigger balls at the corners. That way one could see that the closest corner which is nearest is at the centre. Would it be possible to have a version with lighter shading so one could see inside better? I'd like if there was a bigger version of the last picture on the tesseract page. Thanks very much Dmcq (talk) 11:53, 30 October 2008 (UTC)

OK I'll try to render one without the colorings. It's really tricky to get just the right amount of shading so that the face is visible, yet not have it obscure what is behind. It's not too bad with the tesseract, but with things like the 120-cell, it's much harder to get it right.—Tetracube (talk) 16:24, 30 October 2008 (UTC)

I tried editing the picture in PaintshopPro and using a function called clarify twice at its maximum I got something which I think shows the interior very well, I'll mess around a bit more later on when I have some time and upload it. I notice now that it has been rendered using distances in 3D and there is very little or no 4D perspective so the centre ball is smaller than the ones which are nearest in the 3D image - you might trying upping the 4D perspective instead sometime and see how you like it. Another idea which might work for the larger figures you have is either to have the colour fade more on the nearer side of the 3D image or else fade more for the further away parts in 4D, don't know how that would work out.

The program I wrote to make these projections does scale vertex radii by their distance from the 4D viewpoint, although this effect is not really noticeable because it gets mostly reversed when projecting from 3D to the 2D screen. I could try to reduce the distance from the 4D viewpoint to the polytope; this will exaggerate the perspective distortion and make the nearest vertex larger (but it will also distort the hull of the image, so it can only be done to a certain extent). I have thought about making ridges more transparent as they make larger angles with the viewpoint (the idea being that ridges on the 4D limb of the polytope will be at 90° angle with the viewpoint), but I haven't gotten around to actually implementing this yet.—Tetracube (talk) 18:42, 30 October 2008 (UTC)

OK, here's a testing render:

 

The nearest vertex is highlighted in red, and the other vertices have been omitted. Let me know what you think. I haven't brought the 4D viewpoint any closer to the polytope, but I think omitting the outer vertices should have made this clear enough.—Tetracube (talk) 19:06, 30 October 2008 (UTC)

Yes that's nice, does tell them what's what. Gotta go now. Dmcq (talk) 19:19, 30 October 2008 (UTC)

Here's a demo of applying the PaintshopPro clarify operation set to maximum once

 

I think it demonstrates a little post processing could help to make things more visible. Dmcq (talk) 08:28, 31 October 2008 (UTC)

Well, or I could have just rendered the image with higher transparency values. :) What do you think, should this projection be added to Tesseract or Fourth dimension?—Tetracube (talk) 18:38, 31 October 2008 (UTC)

I think I'd add the one picture to tesseract with a short description and a poitner to fourth dimension for a fuller explanation. I did some editing of that last picture in Fourth dimension, a clarify and copy over of the central red sphere from the other picture, it seemed to just need a left right mirror.

 

Hope those people who catch you out for adding extra missiles into news pictures don't get me, photshopping I believe it's called :) Dmcq (talk) 19:42, 31 October 2008 (UTC)

Just looking at that picture again I couldn't quite figure out what the shadow at the bottom left in the red cube is from. Dmcq (talk) 20:26, 31 October 2008 (UTC)

The shadow is cast by the light source somewhere above and behind the viewpoint, to the right. It's caused by those solid edges and vertices... maybe I should render it with no_shadow instead.—Tetracube (talk) 22:49, 31 October 2008 (UTC)

I added that last picture to the gallery in Tesseract after trimming off some of the white space around it. Dmcq (talk) 02:07, 7 November 2008 (UTC)

Nice catch lol. But Frank Morris must have spent all that time alone in his cell doing something. SpinningSpark 20:13, 31 October 2008 (UTC)

So you're saying he solved the problem of how to break out of jail by reducing it to the problem of solving a scrambled cube? ;-)—Tetracube (talk) 22:47, 31 October 2008 (UTC)

Hi Tetracube! The cube and tesseract images you made for the Fourth dimension page were truly awesome and they really served their purposes. I've been trying to translate the page to the Chinese Wikipedia (zh:四维空间), but those images are not available there. And due to the fact that I just started contributing to Wikipedia, I'm not autoconfirmed there and cannot upload them. Could you please move/upload those images to Commons, so that they are available on all versions of Wikipedia?

As I said, I'm still a rookie at Wikipedia, so if this action should be requested elsewhere, I sincerely apologize. Wyvernoid (talk) 04:57, 7 November 2008 (UTC)

Hmm, I'm not sure how I can move images to the Commons (or if it is even possible). I'll ask around and see.—Tetracube (talk) 20:05, 7 November 2008 (UTC)

(For self-reference: Wikipedia:Moving_images_to_the_Commons)—Tetracube (talk) 20:19, 7 November 2008 (UTC)

Thanks a lot! =] Wyvernoid (talk) 00:38, 8 November 2008 (UTC)

Thanks for watching out and reverting vandalism on my user page. Nsaa (talk) 17:31, 13 November 2008 (UTC)

Thanks for you note regarding this user. I don't think we need to worry about it. Probably better that he vandalize the warning than vandalize mainspace articles. : ) If he keeps vandalizing, he'll get blocked. TimidGuy (talk) 20:35, 18 November 2008 (UTC)

Hi -- you just welcomed me, and I see you're interested in vandalism. I have some questions -- I've looked around in the FAQs a little and probably this issue is addressed *somewhere* but I didn't run into it.

In looking at a Wikipedia entry recently I noticed that the page contained a reference to the subject's "spouse." The subject is not married so I deleted the reference. I did a little Googling and found out that there's been some blog gossip about the subject and a possible relationship, but it seems mostly to be gossip. Today I visited the Wikipedia entry again and noticed that the edit I deleted had been essentially restored, but now the person was listed as the subject's "domestic partner."

The subject of the Wikipedia entry is a political figure who is a single woman. She is not a member of any domestic partnership. Again I removed the edit.

Is the persistent addition of this gossip considered vandalism? Should I be going through the process of reporting it as such? Gilajones (talk) 21:43, 18 November 2008 (UTC)

Wikipedia requires that content be verifiable, so this excludes rumors and unsubstantiated claims. Reverting such edits is right. However, they do not constitute vandalism. Vandalism is only when a page is being defaced (such as removal of content for no reason, adding of gibberish or obscenities, or malicious altering of facts); Wikipedia prefers to assume good faith in edits.

But two editors continually reverting the same edit may be the start of an edit war, which should be avoided. The way to deal with this is to go to the article's talk page (click on the "discussion" link at the top of the page) and start a discussion on why you think this rumour should be removed (it is only a rumour, and not substantiated), and ask the other party to provide a reliable source for it (see Wikipedia:Dispute resolution). If they fail to respond but persist in re-adding the same rumour, you may want to ask an administrator to protect the page from being edited by anonymous editors (if the rumor is persistently coming from an IP, which is usually the case for such cases).—Tetracube (talk) 00:46, 19 November 2008 (UTC)

Thank you! I had already made a Talk comment but have now modified it according to your suggestions. I appreciate the info! Gilajones (talk) 01:59, 19 November 2008 (UTC)

Hello Tetracube!

I've added the coordinates of the tetrahedral cupola; but it still misses the dodecahedral cupola... Padex (talk) 18:33, 23 November 2008 (UTC)

Hi! I've thought that blue is nicer than light brown and that blue type looks not very good with brown background. I'm interested in mathematics, especially in 4D geometry and I'd love to do something useful on any article. Unfortunately, I can't write in English as good as it's needed to write and edit mathematicial articles. Anyway, sorry for making mess. 83.142.122.69 (talk) 12:07, 22 December 2008 (UTC)

No problem, just that usually when we make such stylistic changes, we want to keep consistency across all related articles. We can discuss this with other contributors to those articles (mainly the polychoron articles) and see if we should adopt this new coloring scheme. If we do, you could help us update some of the articles (there are about 60+ of them).—Tetracube (talk) 17:15, 22 December 2008 (UTC)

Consistency was my primary issue. Indeed, there are some 60+ articles. At some point I'd like to convert them to a template-database, in which cases a change to the primary template could change the colors in all. Tom Ruen (talk) 17:31, 22 December 2008 (UTC)

Good idea!! Rather than editing 60+ articles by hand, why not we spend our energy now to create said template, instead of needing to go over 60+ articles now to manually edit their color scheme, and then have to go over them again to convert them to use the new template?—Tetracube (talk) 17:33, 22 December 2008 (UTC)

Yes, and another issue is consistency of content as well, and I admit different classes of polytopes - regular vs uniform vs other (and honeycombs too), might have different content, so it might be worth making a template table now for the regulars. There's two levels possible. One is a template table. The other is a template-database on top, and a bit confusing to understand. The first is easy, just like the Template:Infobox polyhedron, just have to decide what to include. Tom Ruen (talk) 18:20, 22 December 2008 (UTC)

Okay, here's a test: Template:Infobox Polychoron, quickly tried to take elements given in the regular polychora anyway. Tom Ruen (talk) 18:32, 22 December 2008 (UTC)

And tested in Tesseract now. Tom Ruen (talk) 18:42, 22 December 2008 (UTC)

I'd like to help with adding this box to the articles. Then we would discuss the colour. By the way, we would make articles about regular pentachordon more similiar to one other. There are many differents between these articles e.g. with images (many types of arrangement, lack of some images - like net - in a few articles). We would make a model of table for images and use it in these articles. 83.142.122.69 (talk) 19:40, 22 December 2008 (UTC)

It looks good. Are we ready to put this on all the uniform polychoron pages?—Tetracube (talk) 02:56, 24 December 2008 (UTC)

There's some variations needed, regular have some more information than the uniform ones. Petrie polygon, and dual I guess. There's some way to make parameters optional. Otherwise multiple versions could be made. Maybe existing one should be renamed to Template:Infobox Regular polychoron? Maybe my argument names are not well chosen? Lots to worry about before duplicating something too much. Tom Ruen (talk) 04:05, 24 December 2008 (UTC)

I can see that you posted a message on my talk page regarding fourth dimension. I revised it because to me there wasn't enough information, so I added information about vectors. Please Reply. --219.78.119.49 (talk) 01:26, 22 February 2009 (UTC)

I have a question about a section in an article:

http://en.wikipedia.org/wiki/Ken_Calvert#Legislative_Accomplishments

I've done some minor editing to Wikipedia but am still generally a novice, hence my question. It seems to me that the section is more of an advertisement for E-Verify than information about the individual's legislative accomplishments.

What do you think? I'm considering re-writing the section as follows:

In 1995, Rep. Calvert introduced H.R. 502, which was later included in the immigration reform bill, H.R. 2202. [5] The immigration reforms were later wrapped into the FY1997 Omnibus Appropriations Act.

Rep. Calvert is the original author of [E-Verify], a program that enables employers to check the work authorization status of newly hired employees. Rep. Calvert has introduced legislation in the 111th Congress to make use of E-Verify mandatory. [7]

I'm trying to stay true to the spirit of Wikipedia, which is why I ask for your advice. Thanks. 75.36.66.4 (talk) 00:57, 1 March 2009 (UTC)

Yes, the current 2nd paragraph does sound more like an advertisement than an encyclopedic description. I think your rewording is much better. Hope that helps.—Tetracube (talk) 22:01, 1 March 2009 (UTC)