Talk:Uniform polyhedron

message: Okay, given these text below was incomplete (bad links), I moved it below until it can be sorted out or safely deleted.
Tom Ruen 06:20, 22 February 2006 (UTC)
thread_title:  REMOVED SECTIONS BELOW 

message: As an experiment, I regrouped the octahedral polyhedra by "convex hull" vertex arrangements, and named groups like polychoron defined terms.
I'm not sure if the terminology applies like this, but seems consistent anyway.
By "convex hull", I mean taking the vertex set and adding faces by the convex hull. This mostly defines a single vertex geometry, but can also define topologically similar polyhedra with nonregular faces.
Example (Common 4.6.8 topology)   
Obviously the same thing can be done with the Icosahedral symmetry, although takes a bit of work!
Tom Ruen 01:06, 26 February 2006 (UTC)
replies: text: Okay, I regrouped Icosahedral as well. I also subgrouped like "small truncated" for smaller truncations, although visually I can't tell how many categories could be created like this. ALSO I expanded the tetrahedral section similarly, including octahedron/tetrahedron with higher symmety, but also tetrahedral symmetry if different symmetry face coloring used (and created :image:snub tetrahedron.png for icosahedron]] as an example too. Tom Ruen 02:59, 26 February 2006 (UTC)

text: Maybe I'm done for the day, with dihedrals as well, and two new images :Image:tetragonal prism.png and :image:trigonal antiprism.png. I also tried term irregular' for vertex arrangements with convex hull faces which are not regular polygons. Seems reasonable, even if there's DIFFERENT types/poroportions of irregulars! Tom Ruen 04:15, 26 February 2006 (UTC)
thread_title:  Octahedral symmetry 

message: oh the embarrassment, to get caught confusing Greek with Latin in that way, when I'm usually the pedantry police!  —Tamfang 06:47, 9 August 2006 (UTC)
thread_title:  undecim, hendeca 

message: I'm not sure moving the symmetry subsections "up" one level was an improvement. The major section heading indicates a subsequent listing by symmetry, so it seems reasonable for those listings to be subsections of that section. I won't revert the change, however, unless further discussion here indicates that others share me feelings. Paul D. Anderson 22:55, 3 September 2006 (UTC)
replies: text: I agree – and like you, I wasn't gonna bother moving it back merely to please myself.  —Tamfang 23:48, 3 September 2006 (UTC)

text: I agree also, held off reverting, but since I made the sections, I'll please myself and reverted it ! :) Tom Ruen 01:03, 4 September 2006 (UTC)
thread_title:  Subsections 

message: I saw some minor errors with number (singular/plural) and possessive in the large table under Convex forms and fundamental vertex arrangements, and what seemed to be a cut-and-paste error, and I fixed them; but I'd forgotten to sign in. Some geometer, please make sure my changes didn't introduce errors. -- Thnidu (talk) 00:57, 15 June 2008 (UTC)
thread_title:  grammar cleanup 

message: I wanted to expand the Wythoff construction of the convex forms so I moved the nonconvex forms to a subarticle. This is reasonable since there's very limited explanation of what the nonconvex forms are at all so far.
Currently it's a bit of a mess while I rework it. It might be better to move the convex forms also to a subarticle and make this article a shorter summary. So, I'll see what I can do in the coming days to get it cleaned up in a better way.
Tom Ruen (talk) 20:46, 31 July 2008 (UTC)
thread_title:  Reworking sectioning 

message: I'm working on some stereographic projections of the convex uniform polyhedra (as spherical tilings), and got caught short on time for now. I still need to clean up and decide how to present, but thought I'd share a summary (quick&messy) compilation here since they are pretty: 
:
* Columns left to right are: Regulars, truncations, rectifications, cantellations, and omnitruncations. 
* The regular forms by row from top to bottom are: tetrahedron, cube, octahedron, dodecahedron, icosahedron. 
** The rectified, cantellated, omnitruncated forms are presented from two different face centers for the regular-dual pairs. 
* There's no snubs yet, or prisms. The faces are colored to match the uniform polyhedra at Uniform_polyhedron#Summary_tables. 
* I'll also make some Schlegel diagrams too (linear edges).
* It's funny to me I've not seen these complete projections anywhere. The duals are also pretty, but single colored by face symmetry.
* A large part of my motivation is comparison with the uniform polychora which can only be displayed as 3d projections. 
*:For example, I started a 3d/4d comparison at: 120-cell#The_Schlegel_diagram_projection
Tom Ruen (talk) 18:19, 14 August 2008 (UTC)
replies: text: Hm, some of the outermost arcs look noncircular; did you fudge them so as not to have to reduce the inner faces too much?  —Tamfang (talk) 04:21, 22 August 2008 (UTC)
replies: text:  There's no fudging the lines, pure computation, although I did "visually center" the orientations of the projection so the symmetrical arcs will not be identical. I agree many of the arcing edges seem to be elliptical. I'll check the calculations to see if something is wrong, but pretty simple so I'm not sure. Tom Ruen (talk) 23:14, 23 August 2008 (UTC)

text:  I looked at my code and found I DID have a "fudge factor". This perspective is actually slightly above the sphere (by 1% of the radius). Apparently this squishes the outer most edge arcs in the largest forms. I'll reduce the factor to 0.01% for my "real" uploads later. The tolerance is mainly for "vertex-first" projections, so everything is in front of the view. Tom Ruen (talk) 21:58, 24 August 2008 (UTC)
thread_title:  Stereographic projection 

message: I disapprove of "[p,q]-hedron", which I guess is yet another example of using hedron ('face') as a synonym for polyhedron ('[thing with] many faces').  A {p,q} does not have [p,q] faces, whatever that would mean. —Tamfang (talk) 20:00, 24 September 2010 (UTC)
thread_title:  another complaint from the language purist 

message: I've now spent something like two hours trying to find my specific polyhedron. It's *really* hard when you start with descriptive qualities. And I know this isn't really the place where I should start discussing the issue, this being far too specific. But please indulge me, and help the issue along, since I probably couldn't carry this much further myself.
As background, my problem was that I would have liked to find the precise polyhedron which you get by twisting the bottom of a cube 45 degrees against its top. I *know* it has a name, and quite a lot of theory associated with it as well. It's bound to be on Wikipedia, somewhere. Yet I don't seem to be finding it. Evenas it's pretty crucial wrt an audio technology post I'm right now trying to respond to.
As such, polytopes should in mind be more easily findable. Better indexed. I suggest all of the polytopes/commonly-known-simplex-complexes should be thoroughly and visibly indexed by a) vertex count, b) edge count, c) face count, d) all of the higher order counts for higher dimensional simplex-complexes, e) the usual topological integer invariants such as the Euler one, but also a dozen more, where applicable, f) by the name of the attached symmetry group, e) systematically crosslinked by known derivatives/duals/biduals/twisted forms/whatnot that we know from literature. And so on. I think the topics should be systematically tagged, so as to be systematically crosslinked using automatic means, when the time comes.
My point is that most of this sort of tagging could be done purely mechanically. Most of the crosslinking could be about the same thing, if computationally heavy. And yet, it could help countless people find their very basic, nicest mathematical abstraction in the end -- I mean, my rant started with a fucking platonian solid, and didn't go beyond its slightly twisted form. This is stuff that a first grader with a cubical piece of Play-Doh could want to know about... Decoy (talk) 03:11, 29 July 2011 (UTC)
replies: text: Try square antiprism. It is listed in this article, section Uniform_polyhedron#.284_2_2.29_D4hdihedral_symmetry. SockPuppetForTomruen (talk) 01:30, 30 July 2011 (UTC)

text: What, by the way, is a bidual? —Tamfang (talk) 08:47, 23 August 2011 (UTC)
thread_title:  I'd like to find my polyhedron! 

message: I have created and uploaded this 19 [sic]-second animation showing the convex uniform polyhedra:
I had in mind that it could be used on this page. I'm afraid the dithering isn't nice (it was done by the encoder, ffmpeg). I could try re-rendering with a more restricted range of shades, or flat-shade it instead. It could take a different path through the graph of truncations/cantellations/snubifications, if anyone has an opinion on that. Buster79 (talk) 19:00, 10 March 2015 (UTC)
thread_title:  Animated gif