Talk:Regular polyhedron

message: I hope I haven't upset anyone's careful organization of articles regarding polyhedra by replacing the former redirect for this page with a brief descriptive article instead. It seemed like a good idea to me, but I know that Wikipedians have a highly variable sense of "rightness". If I've undone someone else's good work I apologize. andersonpd 01:15, 3 August 2006 (UTC)
replies: text: I think you are absolutely right. Just moved some more stuff over. Way still to go! Steelpillow 22:14, 1 February 2007 (UTC)
thread_title:  New article 

message: I have reverted the recent changes by User:Ppatel43026 because:
#The meaning of face-transitive is that all faces are identical - there is no need to repeat this definition.
#Information on Euler's formula belongs in the planar graph article, which has a section on Euler's formula.
#The style is unencyclopedic (e.g. "Euler was a busy man"); there are numerous digressions; references are incomplete.
Gandalf61 09:21, 18 April 2007 (UTC)
thread_title:  Explanation of reversion 

message: User:4 has just added some "topological" examples to the list of regular polyhedra. This makes me wonder, what should be the scope of this article? If we address these hyperbolics then what about the elliptic, the infinite skew, the multiply-wrapped and so on? Or, should we stick with the nine elementary examples that are regular in any locally Euclidean space? I think that the History section could usefully summarise/link to articles on the more exotic types, but I do feel that there are benefits in the main article to the previous treatment of only discussing the nine in any detail. — Cheers, Steelpillow (Talk) 18:11, 30 August 2011 (UTC)
replies: text: I'd lead to keeping the basis 5+4, and these so-called topological ones seem like trouble - mixing pentagons and pentagrams. I have thought to add the regular skew polyhedra to list of regular polytopes, but still sorting out the finite ones! SockPuppetForTomruen (talk) 02:16, 31 August 2011 (UTC)

text: I expanded the section, showing faces, and added finite skew regular polyhedra. I wondered the regular tilings as infinite polyhedra deserve a section too, but added an intro statement at least. The whole thing needs a look, to see how the following sections are limited by each extended solution class. Maybe, if these cause too many conflicts in the wider sections, these should instead be added as subsections to Regular_polyhedron#Further_generalisations? SockPuppetForTomruen (talk) 00:49, 1 September 2011 (UTC)
replies: text: Tom, not quite sure how your addition of yet more examples relates to your comment that "I'd  lead to keeping the basis 5+4". It appears to me that you have just done the exact opposite, or do I misunderstand? BTW, these "topological" examples are all about regularity of abstract structure - they do not have geometric regularity. Problem with enumeration is, there are shedloads of the beasts, for example User:4 has not mentioned any of the elliptic examples such as the hemicube, hemidodecahedron, hemicosahedron, etc. Also the theory is quite extensive and esoteric - see for example McMullen & Schulte's book Abstract regular polytopes. So I am really in favour of returning to my original approach: cut back the main article to where it was and, in the Further generalisations section, stick to short remarks and reference out with links to the more specialised articles. Otherwise this article will just sprawl and sprawl, losing its elementary focus in the process. Any objections? — Cheers, Steelpillow (Talk) 10:56, 1 September 2011 (UTC)

text: Yes, I'm a contradiction, rethought and attempted to expand to see how it looked, maybe because I was excited about the skew forms. I tried moving the new sections inside of Further generalisations. Seems good to me, although I agree these sections could be cut down further. SockPuppetForTomruen (talk) 17:55, 1 September 2011 (UTC)
replies: text:  That's working for me. I have tidied up a bit and abandoned the description "topological polyhedron" in favour of "abstract polyhedron". The latter term has a precise mathematical meaning, whereas topologists talk about various incompatible types of object as "polyhedra". Once fleshed out, the "Abstract regular polytope" section can be either moved to its own article or merged into the abstract polytope article. — Cheers, Steelpillow (Talk) 20:42, 1 September 2011 (UTC)

text: Good, abstract is much better! I merged the infinite/finite skew polyhedra sections. Should we include the regular projective polyhedron: hemicube, hemi-octahedron, hemi-dodecahedron, hemi-icosahedron? Also there's the hosohedron {2,n}, and dihedron {n,2} which are degenerate polyhedra, except as spherical tilings. I guess these are all covered under abstract regular polytope, as a section of abstract polytope. SockPuppetForTomruen (talk) 21:55, 1 September 2011 (UTC)
replies: text: The hosohedra and dihedra are best introduced after spherical polyhedra, as they can be realised in this form. I'm not sure whether to discuss the regular spherical polyhedra under History or Further Generalisations. — Cheers, Steelpillow (Talk) 21:42, 2 September 2011 (UTC)
replies: text: I've placed them under Further Generalisations for now, because we have to include them somewhere, and there's not much stuff about spherical polyhedra in the History section. Yes, there are the Scottish balls, but those are doubtful - many of them aren't Platonic solids, and the most famous set of Platonic solids among them has a hoaxed octahedron and icosahedron. Double sharp (talk) 06:51, 31 May 2012 (UTC)
thread_title:  Enumeration of regular polyhedra 

message: A regular polyhedron is said to be vertex transitive, but the regular star polyhedra aren't (the number of edges meeting in a vertex is not independent of the vertex), so there is a notational problem there.  — Preceding unsigned comment added by 161.116.84.155 (talk) 15:43, 15 March 2012 (UTC)
replies: text: Can you give an example of a regular star polyhedron where the number of edges meeting in a vertex is dependent on the vertex ? Are you sure you are only considering true vertices, and not including the "false" vertices where sides intersect but do not form a vertex ? Gandalf61 (talk) 15:49, 15 March 2012 (UTC)

text: I replied here Talk:Kepler%E2%80%93Poinsot_polyhedron#Regular polyhedra, explaining the "false vertices" also. Tom Ruen (talk) 19:24, 15 March 2012 (UTC)
thread_title:  regular star polyhedra 

message: Planar apeirohedra aka regular tilings should go on the page, especially since Regular skew apeirohedra are already here.  — Preceding unsigned comment added by 2A01:E35:2FB0:2D10:A9F0:4CDC:F195:40A1 (talk) 11:07, 18 November 2020 (UTC)
thread_title:  Regular Tilings 

message: I was wondering why the SVG images of the Platonic solids were inferior to the JPEG. I didn't see anything in WP:IUP#FORMAT that would seem to be the reason. If there's something wrong with the SVGs, I might try to fix them. AquitaneHungerForce (talk) 13:15, 15 January 2024 (UTC)
replies: text: To see which image is superior, your have to look at the images – not at some page about file formats in general. Files like :File:Tetrahedron.jpg have 3D edges, while those like :File:Tetrahedron.svg have flat lines as edges. The JPGs are good quality, and the SVGs are poor imitations. No file format has any inherent advantage for illustrating an article. So the images with better quality should be used. --Watchduck (quack) 17:52, 16 February 2024 (UTC)
replies: text:  Thanks. That's hard too see. I will make versions of the SVGs with 3D edges and adjust them in the article. AquitaneHungerForce (talk) 17:57, 16 February 2024 (UTC)
replies: text: That is not what SVG is for, and the result will be be inferior to a raster graphic. Why would you want to replace the JPGs, when they are good? Did anyone convince you, that SVG is somehow the best file format? I suggest not to believe that kind of thing. --Watchduck (quack) 18:58, 16 February 2024 (UTC)
replies: text:  I'd like to replace them because they look bad. They have a annoying white square around them and (on my screen) visible artifacting. At least in my opinion the SVGs already look better, but it would be nice to have an image that looks nice for everyone. Is there something else wrong with an SVG that would make it inferior to a high quality raster? AquitaneHungerForce (talk) 19:53, 16 February 2024 (UTC)

text:  Here's the 3D version of the cube. If you have any suggested changes I can adjust it and then complete the set. AquitaneHungerForce (talk) 20:54, 16 February 2024 (UTC)
replies: text: Yes, the white background is bad. Raytraced images should be PNG, not JPG. Your SVG looks better than I expected. I suggest, that you overwrite the current SVGs with your improved versions. Overwriting is sometimes abused, but this is exactly what it is for. (BTW, maybe you could upload a little screencast as a tutorial? The tetrahedron would be ideal for that.) --Watchduck (quack) 21:21, 16 February 2024 (UTC)
replies: text: Here's a screencast: :File:3D Edges in Inkscape demonstration.webm. However I ended up not being satisfied with the tetrahedron in the video so I redid that from scratch. I'll finish and upload when I have some more time. AquitaneHungerForce (talk) 22:35, 24 February 2024 (UTC)
thread_title:  jpg images