Talk:Polyhedron

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Contents 1 Quasi-regular 2 Archimedean stellations 3 Bit of a shake-up 3.1 Planned changes 3.2 Definition 4 More pictures of polyhedrons at the top of the page? 5 Books on polyhedra

[edit] Quasi-regular

Could someone please improve this article? Towards the begining it states that quasi-regular polyhedra are edge- and vertex-uniform, but then later it makes a statement about how the icosidodecahedron cuboctahedron are quasi-uniform with the additional property of being edge-uniform. This seems contradictory. Please help. superscienceman 18:26, 3 October 2006 (UTC)

I changed the quasiregular definition to only edge-uniform, since there's two classes vertex-uniform and face-uniform polyhedra, which are actually duals of each other. I agree it needs further work. Tom Ruen 22:28, 3 October 2006 (UTC)

I also removed constraint that semiregular can't be edge-uniform, since all of the Archimedean solids, prisms, antiprisms can be considered semiregular. Tom Ruen 22:33, 3 October 2006 (UTC)

I have created a stub page for quasiregular polyhedron. I am also asking around about the definition of "quasiregular" - it's yet another of those messy areas. Steelpillow 12:13, 8 January 2007 (UTC)

[edit] Archimedean stellations

I changed the following sentence to avoid the problematic term "semiregular", but I think there are other issues -- or at least, I don't understand it:

Of the 39 non-convex, non-prismatic uniform polyhedra, 17 are stellations of Archimedean solids.

There are 75 non-prismatic uniform polyhedra. Of these 18 are convex -- the Platonic and Archimedean solids. That leaves 57 nonconvex, nonprismatic uniform polyhedra (either all of which, or none of which, are semiregular by most definitions of the term.) Where does the number 39 come from? Also, which 17 are stellations of Archimedean solids (admittedly that enumeration doesn't belong in this article) and what's the source of this fact (that does belong!) -- Rsholmes 16:24, 22 December 2006 (UTC)

No one's come to the defense of this statement, which I believe is either wrong or badly stated, so I'm deleting it. -- Rsholmes 00:05, 8 January 2007 (UTC)

[edit] Bit of a shake-up

I've just rearranged the headings a bit to make a more ordered hierarchy, also tidied up a little of the semi-regular confusion and a few other bits. The main section is still pretty unwieldly. I think some of the lists of names should go (eg various uniform polyhedra), just leaving the thumbnails behind. Also, I think it better to list each type of uniform and its duals in the same sub-section, but I don't have time right now.

Well, I've had another bash today. :-) Much more to be done though :-( Steelpillow 13:08, 8 January 2007 (UTC)

Finally, does anybody know how to archive the older bits of this Discussion page? It's getting a bit top-heavy.

Cheers, Steelpillow 22:11, 7 January 2007 (UTC)

I've done little but cleanup myself in this article in the past, although I suppose I did get the image zoo going here. I moved the pre-July talk to an archive subpage.

I finally got a Wythoff symbol article going this weekend, not great but a fair start, and pretty spherical polyhedra images! Tom Ruen 01:06, 8 January 2007 (UTC)

[edit] Planned changes

Thinking of a few more big changes (as I find the time):

• Replace the phrase 'classical polyhedron' with 'traditional polyhedron'. Somehow 'classical' suggests an accepted terminology (as in say 'classical architecture') which is not so.
• Shrink the info on the various uniform polyhedra, as this should all be covered by the Uniform polyhedra page.
• As mentioned above, combine the Uniforms and their Duals in a single strand.

Any objections? Steelpillow 09:39, 12 January 2007 (UTC)

Sounds good to me. Tom Ruen 10:19, 12 January 2007 (UTC)

Phew! All done in a rush. Any better? Still some more shrinking to do. Steelpillow 20:07, 12 January 2007 (UTC)

Well, done some more of that now! Have I pruned too much info from "Symmetrical polyhedra"? It was all duplicated on other pages. Still needs more tidying, tho. Steelpillow 20:17, 27 January 2007 (UTC)

[edit] Definition

I don't like the new definition section much. Saying it's a 3-dimensional polytope doesn't help anyone unless they already know what a polytope is -- in which case they probably already know what a polyhedron is. Certainly by reading onward one can get a sense of what a polyhedron is, but really there should be an accessible, helpful definition right up at the top. Under the heading "Definition"! -- Rsholmes 20:09, 12 January 2007 (UTC)

Better now? Steelpillow 14:57, 13 January 2007 (UTC)

Yes it is, thanks. I still think there's room for improvement though. My feeling is this article is mostly going to be read by lay people who don't need to hear right from the outset about nonplanar faces, nonlinear edges, and nullities. This is not to say they can't be mentioned close to the top, but I'd advocate starting off with a (one of the!) traditional definition of a polyhedron -- e.g. a volume of 3-dimensional space bounded by polygons that meet at their edges. Give a paragraph about that, and then say "More generally, ..." et cetera. -- Rsholmes 17:30, 13 January 2007 (UTC)

OK. Try this...

BTW, anybody got a suitable pretty picture of one to put up there at the start? Steelpillow 20:48, 13 January 2007 (UTC)

I'd probably drop nullity definition, not referenced anywhere else in the article. Tom Ruen 19:16, 18 January 2007 (UTC)

The definition is incomplete without it, but I don't think it's worth discussing any deeper on this page. I've linked it to the Abstrct Polyhedra bit. Steelpillow 18:16, 19 January 2007 (UTC)

[edit] More pictures of polyhedrons at the top of the page?

Is the one picture, that of the dodecahedron, sufficient? kabbelen 04:23, 1 March 2007 (UTC)

More would be good, perhaps a row of small-ish ones. Do you have time to put together some nice ones? Steelpillow 19:54, 1 March 2007 (UTC)

I have time, but I don't know how to put together some nice ones. Is it possible to put a column of images next to the table of contents? kabbelen 18:21, 3 March 2007 (UTC)

I expect that it is possible, but I do not know how. Anybody else...? Steelpillow 21:35, 3 March 2007 (UTC)

Okay, I tried a column of test images in a table. Feel free to change or whatever. Tom Ruen 23:09, 3 March 2007 (UTC)

Nice one, Tom. Tell you what - if one of us gets time, how about a bit more variety in colour and style? Steelpillow 10:50, 4 March 2007 (UTC)

Okay one more improvement. Two columns, added a descriptive category following each. A fair representation, always room for more! :) —The preceding unsigned comment was added by Tomruen (talk • contribs) 03:20, 7 March 2007 (UTC).

I like that a lot. Just one small thought. In my browser (Firefox 1.5) the table border is right up against the introductory text above the Table of Contents. Is there any way to put a few pixels' clear space between them? Steelpillow 20:17, 7 March 2007 (UTC)

Images can be made smaller. It's impossible to decide how big things should be since people run different screen resolutions. My screen is 1280 pixels wide so lots of room. The new IE also does nice automatic shrinking for printing - previously it would just cut things off. Tom Ruen 20:38, 7 March 2007 (UTC)

It's not the size of the images, it's the way Firefox runs the text right up to the table border. Nice to hear that IE is at last learning lessons from Firefox about usability. Steelpillow 10:12, 8 March 2007 (UTC)

Fixed it with a nested table. Steelpillow 17:46, 18 March 2007 (UTC)

[edit] Books on polyhedra

I added this new section. Please help! Especially if you think I've put a book in the wrong subsection. Steelpillow 17:46, 18 March 2007 (UTC)