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The uniform polychora lists are moved here from Polychora. Some things that need to be done:
— Tetracube 07:15, 10 January 2006 (UTC)
How do you like my first table? (I must dash now, will make the others later.) Someone besides me should check it against [1]. -- Anton Sherwood 18:46, 10 January 2006 (UTC)
Hi, I saw the new tables you put in. I see that you've put in all 46 uniform polychora. Cool!
However, I'm not sure about the paragraph on the antiprisms. I question putting the antiprisms here... as far as I know, they are not vertex-uniform, because the vertices on one cell are not congruent to the vertices on the dual cell. I suspect they may belong to a more general category of polychora, but I don't see how they satisfy the requirements of being uniform polychora.
Actually, scratch that. I didn't read the paragraph carefully. Sorry :-)
—
Tetracube
06:07, 11 January 2006 (UTC)
See the paragraph I've just added to "grand antiprism". I'm guessing that analogous forms can be constructed, whose cells are 4n 'n'-antiprisms and 12n2 tetrahedra, which meet part of the definition of uniformity – a symmetry group on the vertices – but whose facets are not uniform. I'd like to add that if someone can confirm it (my 4d geometry is still very weak). — Tamfang 04:06, 13 February 2006 (UTC)
I noticed that the wikipedia style guidelines suggest that article names be singular where possible, rather than plural. Should we rename this page to uniform polychoron instead?— Tetracube 18:51, 27 January 2006 (UTC)
The result of the debate was
Move carried out in accordance with consensus and naming conventions. - Haukur 17:22, 5 February 2006 (UTC)
Should this page be moved to Uniform polychoron?
YES:
NO:
I saw polychora articles updated for new name here. I was thinking, do we want a Category:Polychora or Category:Polychoron or Category:Uniform polychora or Category:Uniform polychoron?
Currently they are under Category:Polytopes which isn't bad, except for not specifying 4D objects, although not much going on above 4D yet! Tom Ruen 06:30, 7 February 2006 (UTC)
Not sure about this header title for a section declaring terminology, but good enough.
I added a definition for snub which seems to be correct for uniform polyhedra, but don't know well how it applies to polychora like snub 24-cell.
Obviously it would be good to have some sequential images or even animations to show these operations. Maybe I can add something sometime, but I don't think I can do all of them. Tom Ruen 02:04, 13 February 2006 (UTC)
Marek Čtrnáct gave me a surprising definition of snub. Start with a polytope whose faces all have even degree, such as an omnitruncate; then you can remove alternate vertices, inserting vertex figures (like rectification but twice as deep). Deform the result as necessary to make it uniform:
Several other convex polychora can be given this treatment but the result cannot be made uniform. Marek didn't go into nonconvex examples. — Tamfang 18:22, 15 February 2006 (UTC)
Hey Tamfang, I just saw your latest edit to the grand antiprism. From the description, it seems that the girthing band of tetrahedra is topologically equivalent to the ridge of the duocylinder, which is topologically isomorphic to the 2-torus; and the two rings of pentagonal antiprisms are topologically equivalent to the duocylinder's two bounding 3-manifolds. This is very interesting. I should like to get hold of the vertices of the grand antiprism so that I can plot its projections into 3-space, to confirm my theory.
Anyway, I'm thinking of moving the info about the grand antiprism into its own page. What do you think?— Tetracube 04:16, 13 February 2006 (UTC)
OK, I've made a draft of the grand antiprism article. Comments?— Tetracube 06:09, 13 February 2006 (UTC)
Hey TamFang... I just noticed that you shortened many of the polychoron names (e.g., "runcinated tesseract" → "runcinated") to "save space". I'm not sure I understand the rationale behind this, since this makes the entry ambiguous and hard to understand. (In the 24-cell section, it can perhaps be inferred; but in the other sections, I'm not sure this is a good idea.) I reverted the 120-cell/600-cell section before I realized what was going on, but I'd like to discuss this before either one of us edits it either way.— Tetracube 15:56, 11 July 2006 (UTC)
Tom, the {3,3,4} and {3,4,3} families share three members, not two, but that makes the total come out wrong ... — Tamfang 18:34, 15 July 2006 (UTC)
In regards to the nonconvex polychora and the Uniform Polychora Project, I'd have to judge it is "unpublished ongoing research" and not clearly defendable within the context of an encyclopedia, ALTHOUGH may be worthy to include on a TALK page, like here!
I might include a statement on nonconvex forms like:
REMOVED TEXT
In regards to the 47 uniform polychora, 18 convex prismatic forms, and infinite set of duoprisms, this appears solid to me, and I'd just like to see more history, and sources. As far as I know the entire content has been extracted from George Olshevsky's website, and his website doesn't contain clear referenced sources. From this article we don't even know WHO discovered these and when!
Well, I hope this opens the door to getting the sources we want here! Tom Ruen 03:47, 15 July 2006 (UTC)
I removed reference to the open research article Uniform Polychora Project and added a draft history section using information above. Unfortunately fuzzy in details, but a start. Tom Ruen 19:32, 15 July 2006 (UTC)
I expanded the new history section and a reference section, selected from the [www.polytope.de] website. That's all I can do now. I'm happy if anyone can expand or improve. Tom Ruen 20:19, 15 July 2006 (UTC)
For what it's worth, the list of alternate names given by George Olshevsky for each convex uniform polychoron demonstrates that more than one mathematician – including John Horton Conway, Norman Johnson, Neil Sloane – has taken an interest. ;) — Tamfang 03:52, 16 July 2006 (UTC)
The University of MN library has a copy of the book by B. Grünbaum, Convex polytopes, 2003 [3] (1st and 2nd editions). I'll try to stop over there adn look at it in the new few weeks. Tom Ruen 22:15, 17 July 2006 (UTC)
Hi all, I've finally found a reference to the paper that describes the uniform polychora (at least, the convex ones). Unfortunately, I don't currently have access to a university library to actually get a copy of this paper, but maybe somebody can do it. The reference is:
This page describes some aspects of the paper, including some references to how the uniform polychora are constructed.
Now, with respect to the more specific semiregular 4-polytopes, the references (also listed on the above site) are:
Somebody with access to these journals can help us look up these articles and check against the material on this page. I hope this helps to ground this article on reliable sources. :-) — Tetracube 06:07, 9 August 2006 (UTC)
As a first test, I added cell/face/edge/vertex counts to the 5-cell family. I'm also interested in adding columns for face counts by type, and cells per vertex, but don't want the table too wide, so I'll leave out for now.
Tom Ruen 21:17, 20 July 2006 (UTC)
There are now stub articles for all of the first 48 forms. If anyone wants to help fill in data, I've put a summary data table at: User:Tomruen/uniform_polychoron_table. This independent source should agree with George O's data at [5] [6] [7] [8] [9], etc, although I've not compared all of them. My spare time is pretty much gone for the rest of August. Thanks! Tom Ruen 04:48, 14 August 2006 (UTC)
I wonder if this should be renamed to Convex uniform polychoron, since there is actually zero content on nonconvex forms?
This would parallel names for convex regular polychoron and convex uniform honeycomb. Polychoron could reference the existence of nonconvex forms.
Tom Ruen 03:02, 18 September 2006 (UTC)
Discussion?
Vote?
See Talk:Cantellated 5-cell if you have interest or opinions on projection terminology. Thanks! Tom Ruen 22:26, 3 January 2007 (UTC)
I added Coxeter-Dynkin diagram for most of the figures, and expanded tables for the prismatic forms. New tables need elements cross-checked for correctness. I'll try to expand some more sample tables at the end for smallest duoprisms. I'm done for the weekend, except maybe a bit of cross-checking...
This article is getting a bit long, but I like them all in one article. Perhaps useful to consider at some point a List of uniform polychora parallel to List of uniform polyhedra. Then this article could have tables reduced to less information perhaps.
Tom Ruen 14:34, 20 January 2007 (UTC)
Okay, I was too curious so I added the B4 family polychora (from 7. Uniform polychora derived from glomeric tetrahedron B4) , all repeats, but I was curious about how they were related. I added new Y-graph Coxeter-Dynkin diagrams, but had to leave the cells grouped like the {4,3,3} and {3,4,3} families, since I didn't know how they are related. I'll look for more information about these. Tom Ruen 05:21, 21 January 2007 (UTC)
Last effort - added Coxeter group names to every family - need to explain more, but seemed useful to include. Tom Ruen 05:43, 21 January 2007 (UTC)
I'm trying out some new images, making some consistent sets between truncated forms within each class. First test run done on simplex family, centering on cell pos. 3, and showing cells at pos. 0. Seems a good start. Tom Ruen 03:01, 16 March 2007 (UTC)
5-cell image set:
![]() t0{3,3,3} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 |
Thought on 8/16-cell and 120/600-cell families. Probably best to end up splitting the tables into two by each regular generator (2 tables of 9, rather than one 1 table of 15), duplicating the symmetric forms (bitruncated/runcinated/omnitruncated). This is needed so I can show the truncations from each direction and the middle forms will have two images with different cells visible. Tom Ruen 03:57, 16 March 2007 (UTC)
8-cell/16-cell image set:
![]() t0{4,3,3} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 | |
![]() t0{3,3,4} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 |
![]() sr |
[This paragraph is ambiguous in the extreme. I THINK this is what is meant:]
There are three families of uniform polychora that are considered prismatic:
These prisms generalize the properties ...
[Under each of these 3 heading belong the following lead sentences:]
Polyhedral prisms
The first family contains three subsets: Tetrahedral prisms, Octahedral prisms, and Icosahedral prisms. They are the most obvious family of prismatic polychora, i.e. products of a polyhedron ...
Duoprisms: ...
The second family is the infinite set of duoprisms–products of two regular polygons. The snubbed form–prisms of anti-prisms–is excluded.
Their Coxeter-Dynkin diagram ...
Polygonal prismatic prisms: ...
The third family contains two subsets: Prismatic prisms and Anti-prismatic prisms. Both subsets are infinite.
The prismatic prisms overlap with ...
The anti-prismatic prisms are constructed ...
[However, I do not want to make edit changes, if I am wrong. Further, I believe "prisms of anti-prisms" are the same as "Anti-prismatic prisms" and should be cross referenced--i.e. "excluded" replaced by "included in the third family".]
18:52, 29 January 2011 Colin.campbell.27
The numbers don't add up.
Where does the "75" come from? Where are they? I can't get to "75 nonprismatic uniform polyhedra" from "64 convex uniform polychora".
Do the two references to "18 convex" refer to the same set of prisms? (I assume they do.)
22 prisms are listed. 5 of them are duplicates (within "[ ]"). 1 of these is the cube-prism/tesseract. Does 18 = 22 – 5 + 1?
Clarification is needed.
18:52, 29 January 2011 Colin.campbell.27
I'm still checking, but here's a first pass list of 3-sphere symmetry groups, in Coxeter's notation (From Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591], mostly from a single table). There's definitely more lower symmetry groups unlisted!
When it looks solid, I'll make an article list List_of_spherical_symmetry_groups (for 2-sphere groups), and link to this under the stat tables for the uniform 4-polytopes. Currently it links to Coxeter group which is really only the pure reflectional symmetries of the Coxeter-Dynkin graphs. Tom Ruen ( talk) 03:13, 24 May 2011 (UTC)
|
|
|
|
|
|
Surely the 17 convex polyhedral prisms (#48 to #64) can't be considered non-prismatic? Double sharp ( talk) 10:05, 6 August 2012 (UTC)
Is the word "alterated" in the article an accepted technical term? I don't find it in dictionaries.
There is a relevant discussion at Talk:4-polytope#Unknown_total_number_of_nonconvex_uniform_4-polytopes — Cheers, Steelpillow ( Talk) 11:05, 19 December 2014 (UTC)
This article is about uniform figures. The section on nonuniform alternations: a) is not relevant, and b) relies on self-published and sparse web content for its citations. This also applies to the recently-added subsection on "scaliform" figures. Is there an established reliable source for all this stuff so it can go somewhere else rather than be summarily deleted? — Cheers, Steelpillow ( Talk) 10:58, 23 December 2014 (UTC)
We have them for all the nonprismatics, and I'm uploading some prismatic examples. Since these are rather prominent visualization aids for the polychora perhaps we could add them in their own column. Double sharp ( talk) 08:14, 8 February 2015 (UTC)
I re-added a short description on the uniform star polychora. The fact that they're on a program (Stella4D) where they can visualized surely makes the claims about their existence credible? If some other mathematician has mentioned them during the last few years, a source would be helpful. – OfficialURL ( talk) 18:26, 21 February 2020 (UTC)
Much of this article is written in obfuscatory language than anyone not intimately familiar with the technical terminology of polytopes is certain will be certain to find confusing.
Additionally, many other things are extremely unclear.
This is very unfortunate, because some Wikipedia writers have made great efforts to fill Wikipedia with extremely comprehensive information about polytopes, and 4-dimensional polytopes in particular.
For example, the very first table of this article is filled with information. But nobody knows what this table is for, because it is entirely unlabeled and has no caption.
I hope anyone who might like to improve this article, and who is familiar with the subject matter and who knows how to write clearly for a non-expert audience, will do so. 50.205.142.50 ( talk) 20:22, 14 June 2020 (UTC)
One sentence reads as follows:
"The 5-cell has diploid pentachoric [3,3,3] symmetry,[7] of order 120, isomorphic to the permutations of five elements, because all pairs of vertices are related in the same way."
But isn't it necessary for — not just all pairs of vertices — but all vertices, as well as pairs, triples, and quadruples of vertices to be each related in the same way ... in order for the symmetry group to consist of all permutations of the vertices? 50.205.142.50 ( talk) 17:17, 26 June 2020 (UTC)
The following Wikimedia Commons files used on this page or its Wikidata item have been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 17:24, 23 August 2022 (UTC)
![]() | This article is rated C-class on Wikipedia's
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The uniform polychora lists are moved here from Polychora. Some things that need to be done:
— Tetracube 07:15, 10 January 2006 (UTC)
How do you like my first table? (I must dash now, will make the others later.) Someone besides me should check it against [1]. -- Anton Sherwood 18:46, 10 January 2006 (UTC)
Hi, I saw the new tables you put in. I see that you've put in all 46 uniform polychora. Cool!
However, I'm not sure about the paragraph on the antiprisms. I question putting the antiprisms here... as far as I know, they are not vertex-uniform, because the vertices on one cell are not congruent to the vertices on the dual cell. I suspect they may belong to a more general category of polychora, but I don't see how they satisfy the requirements of being uniform polychora.
Actually, scratch that. I didn't read the paragraph carefully. Sorry :-)
—
Tetracube
06:07, 11 January 2006 (UTC)
See the paragraph I've just added to "grand antiprism". I'm guessing that analogous forms can be constructed, whose cells are 4n 'n'-antiprisms and 12n2 tetrahedra, which meet part of the definition of uniformity – a symmetry group on the vertices – but whose facets are not uniform. I'd like to add that if someone can confirm it (my 4d geometry is still very weak). — Tamfang 04:06, 13 February 2006 (UTC)
I noticed that the wikipedia style guidelines suggest that article names be singular where possible, rather than plural. Should we rename this page to uniform polychoron instead?— Tetracube 18:51, 27 January 2006 (UTC)
The result of the debate was
Move carried out in accordance with consensus and naming conventions. - Haukur 17:22, 5 February 2006 (UTC)
Should this page be moved to Uniform polychoron?
YES:
NO:
I saw polychora articles updated for new name here. I was thinking, do we want a Category:Polychora or Category:Polychoron or Category:Uniform polychora or Category:Uniform polychoron?
Currently they are under Category:Polytopes which isn't bad, except for not specifying 4D objects, although not much going on above 4D yet! Tom Ruen 06:30, 7 February 2006 (UTC)
Not sure about this header title for a section declaring terminology, but good enough.
I added a definition for snub which seems to be correct for uniform polyhedra, but don't know well how it applies to polychora like snub 24-cell.
Obviously it would be good to have some sequential images or even animations to show these operations. Maybe I can add something sometime, but I don't think I can do all of them. Tom Ruen 02:04, 13 February 2006 (UTC)
Marek Čtrnáct gave me a surprising definition of snub. Start with a polytope whose faces all have even degree, such as an omnitruncate; then you can remove alternate vertices, inserting vertex figures (like rectification but twice as deep). Deform the result as necessary to make it uniform:
Several other convex polychora can be given this treatment but the result cannot be made uniform. Marek didn't go into nonconvex examples. — Tamfang 18:22, 15 February 2006 (UTC)
Hey Tamfang, I just saw your latest edit to the grand antiprism. From the description, it seems that the girthing band of tetrahedra is topologically equivalent to the ridge of the duocylinder, which is topologically isomorphic to the 2-torus; and the two rings of pentagonal antiprisms are topologically equivalent to the duocylinder's two bounding 3-manifolds. This is very interesting. I should like to get hold of the vertices of the grand antiprism so that I can plot its projections into 3-space, to confirm my theory.
Anyway, I'm thinking of moving the info about the grand antiprism into its own page. What do you think?— Tetracube 04:16, 13 February 2006 (UTC)
OK, I've made a draft of the grand antiprism article. Comments?— Tetracube 06:09, 13 February 2006 (UTC)
Hey TamFang... I just noticed that you shortened many of the polychoron names (e.g., "runcinated tesseract" → "runcinated") to "save space". I'm not sure I understand the rationale behind this, since this makes the entry ambiguous and hard to understand. (In the 24-cell section, it can perhaps be inferred; but in the other sections, I'm not sure this is a good idea.) I reverted the 120-cell/600-cell section before I realized what was going on, but I'd like to discuss this before either one of us edits it either way.— Tetracube 15:56, 11 July 2006 (UTC)
Tom, the {3,3,4} and {3,4,3} families share three members, not two, but that makes the total come out wrong ... — Tamfang 18:34, 15 July 2006 (UTC)
In regards to the nonconvex polychora and the Uniform Polychora Project, I'd have to judge it is "unpublished ongoing research" and not clearly defendable within the context of an encyclopedia, ALTHOUGH may be worthy to include on a TALK page, like here!
I might include a statement on nonconvex forms like:
REMOVED TEXT
In regards to the 47 uniform polychora, 18 convex prismatic forms, and infinite set of duoprisms, this appears solid to me, and I'd just like to see more history, and sources. As far as I know the entire content has been extracted from George Olshevsky's website, and his website doesn't contain clear referenced sources. From this article we don't even know WHO discovered these and when!
Well, I hope this opens the door to getting the sources we want here! Tom Ruen 03:47, 15 July 2006 (UTC)
I removed reference to the open research article Uniform Polychora Project and added a draft history section using information above. Unfortunately fuzzy in details, but a start. Tom Ruen 19:32, 15 July 2006 (UTC)
I expanded the new history section and a reference section, selected from the [www.polytope.de] website. That's all I can do now. I'm happy if anyone can expand or improve. Tom Ruen 20:19, 15 July 2006 (UTC)
For what it's worth, the list of alternate names given by George Olshevsky for each convex uniform polychoron demonstrates that more than one mathematician – including John Horton Conway, Norman Johnson, Neil Sloane – has taken an interest. ;) — Tamfang 03:52, 16 July 2006 (UTC)
The University of MN library has a copy of the book by B. Grünbaum, Convex polytopes, 2003 [3] (1st and 2nd editions). I'll try to stop over there adn look at it in the new few weeks. Tom Ruen 22:15, 17 July 2006 (UTC)
Hi all, I've finally found a reference to the paper that describes the uniform polychora (at least, the convex ones). Unfortunately, I don't currently have access to a university library to actually get a copy of this paper, but maybe somebody can do it. The reference is:
This page describes some aspects of the paper, including some references to how the uniform polychora are constructed.
Now, with respect to the more specific semiregular 4-polytopes, the references (also listed on the above site) are:
Somebody with access to these journals can help us look up these articles and check against the material on this page. I hope this helps to ground this article on reliable sources. :-) — Tetracube 06:07, 9 August 2006 (UTC)
As a first test, I added cell/face/edge/vertex counts to the 5-cell family. I'm also interested in adding columns for face counts by type, and cells per vertex, but don't want the table too wide, so I'll leave out for now.
Tom Ruen 21:17, 20 July 2006 (UTC)
There are now stub articles for all of the first 48 forms. If anyone wants to help fill in data, I've put a summary data table at: User:Tomruen/uniform_polychoron_table. This independent source should agree with George O's data at [5] [6] [7] [8] [9], etc, although I've not compared all of them. My spare time is pretty much gone for the rest of August. Thanks! Tom Ruen 04:48, 14 August 2006 (UTC)
I wonder if this should be renamed to Convex uniform polychoron, since there is actually zero content on nonconvex forms?
This would parallel names for convex regular polychoron and convex uniform honeycomb. Polychoron could reference the existence of nonconvex forms.
Tom Ruen 03:02, 18 September 2006 (UTC)
Discussion?
Vote?
See Talk:Cantellated 5-cell if you have interest or opinions on projection terminology. Thanks! Tom Ruen 22:26, 3 January 2007 (UTC)
I added Coxeter-Dynkin diagram for most of the figures, and expanded tables for the prismatic forms. New tables need elements cross-checked for correctness. I'll try to expand some more sample tables at the end for smallest duoprisms. I'm done for the weekend, except maybe a bit of cross-checking...
This article is getting a bit long, but I like them all in one article. Perhaps useful to consider at some point a List of uniform polychora parallel to List of uniform polyhedra. Then this article could have tables reduced to less information perhaps.
Tom Ruen 14:34, 20 January 2007 (UTC)
Okay, I was too curious so I added the B4 family polychora (from 7. Uniform polychora derived from glomeric tetrahedron B4) , all repeats, but I was curious about how they were related. I added new Y-graph Coxeter-Dynkin diagrams, but had to leave the cells grouped like the {4,3,3} and {3,4,3} families, since I didn't know how they are related. I'll look for more information about these. Tom Ruen 05:21, 21 January 2007 (UTC)
Last effort - added Coxeter group names to every family - need to explain more, but seemed useful to include. Tom Ruen 05:43, 21 January 2007 (UTC)
I'm trying out some new images, making some consistent sets between truncated forms within each class. First test run done on simplex family, centering on cell pos. 3, and showing cells at pos. 0. Seems a good start. Tom Ruen 03:01, 16 March 2007 (UTC)
5-cell image set:
![]() t0{3,3,3} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 |
Thought on 8/16-cell and 120/600-cell families. Probably best to end up splitting the tables into two by each regular generator (2 tables of 9, rather than one 1 table of 15), duplicating the symmetric forms (bitruncated/runcinated/omnitruncated). This is needed so I can show the truncations from each direction and the middle forms will have two images with different cells visible. Tom Ruen 03:57, 16 March 2007 (UTC)
8-cell/16-cell image set:
![]() t0{4,3,3} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 | |
![]() t0{3,3,4} |
![]() t0,1 |
![]() t1 |
![]() t0,2 |
![]() t0,3 |
![]() t1,2 |
![]() t0,1,2 |
![]() t0,1,3 |
![]() t0,1,2,3 |
![]() sr |
[This paragraph is ambiguous in the extreme. I THINK this is what is meant:]
There are three families of uniform polychora that are considered prismatic:
These prisms generalize the properties ...
[Under each of these 3 heading belong the following lead sentences:]
Polyhedral prisms
The first family contains three subsets: Tetrahedral prisms, Octahedral prisms, and Icosahedral prisms. They are the most obvious family of prismatic polychora, i.e. products of a polyhedron ...
Duoprisms: ...
The second family is the infinite set of duoprisms–products of two regular polygons. The snubbed form–prisms of anti-prisms–is excluded.
Their Coxeter-Dynkin diagram ...
Polygonal prismatic prisms: ...
The third family contains two subsets: Prismatic prisms and Anti-prismatic prisms. Both subsets are infinite.
The prismatic prisms overlap with ...
The anti-prismatic prisms are constructed ...
[However, I do not want to make edit changes, if I am wrong. Further, I believe "prisms of anti-prisms" are the same as "Anti-prismatic prisms" and should be cross referenced--i.e. "excluded" replaced by "included in the third family".]
18:52, 29 January 2011 Colin.campbell.27
The numbers don't add up.
Where does the "75" come from? Where are they? I can't get to "75 nonprismatic uniform polyhedra" from "64 convex uniform polychora".
Do the two references to "18 convex" refer to the same set of prisms? (I assume they do.)
22 prisms are listed. 5 of them are duplicates (within "[ ]"). 1 of these is the cube-prism/tesseract. Does 18 = 22 – 5 + 1?
Clarification is needed.
18:52, 29 January 2011 Colin.campbell.27
I'm still checking, but here's a first pass list of 3-sphere symmetry groups, in Coxeter's notation (From Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591], mostly from a single table). There's definitely more lower symmetry groups unlisted!
When it looks solid, I'll make an article list List_of_spherical_symmetry_groups (for 2-sphere groups), and link to this under the stat tables for the uniform 4-polytopes. Currently it links to Coxeter group which is really only the pure reflectional symmetries of the Coxeter-Dynkin graphs. Tom Ruen ( talk) 03:13, 24 May 2011 (UTC)
|
|
|
|
|
|
Surely the 17 convex polyhedral prisms (#48 to #64) can't be considered non-prismatic? Double sharp ( talk) 10:05, 6 August 2012 (UTC)
Is the word "alterated" in the article an accepted technical term? I don't find it in dictionaries.
There is a relevant discussion at Talk:4-polytope#Unknown_total_number_of_nonconvex_uniform_4-polytopes — Cheers, Steelpillow ( Talk) 11:05, 19 December 2014 (UTC)
This article is about uniform figures. The section on nonuniform alternations: a) is not relevant, and b) relies on self-published and sparse web content for its citations. This also applies to the recently-added subsection on "scaliform" figures. Is there an established reliable source for all this stuff so it can go somewhere else rather than be summarily deleted? — Cheers, Steelpillow ( Talk) 10:58, 23 December 2014 (UTC)
We have them for all the nonprismatics, and I'm uploading some prismatic examples. Since these are rather prominent visualization aids for the polychora perhaps we could add them in their own column. Double sharp ( talk) 08:14, 8 February 2015 (UTC)
I re-added a short description on the uniform star polychora. The fact that they're on a program (Stella4D) where they can visualized surely makes the claims about their existence credible? If some other mathematician has mentioned them during the last few years, a source would be helpful. – OfficialURL ( talk) 18:26, 21 February 2020 (UTC)
Much of this article is written in obfuscatory language than anyone not intimately familiar with the technical terminology of polytopes is certain will be certain to find confusing.
Additionally, many other things are extremely unclear.
This is very unfortunate, because some Wikipedia writers have made great efforts to fill Wikipedia with extremely comprehensive information about polytopes, and 4-dimensional polytopes in particular.
For example, the very first table of this article is filled with information. But nobody knows what this table is for, because it is entirely unlabeled and has no caption.
I hope anyone who might like to improve this article, and who is familiar with the subject matter and who knows how to write clearly for a non-expert audience, will do so. 50.205.142.50 ( talk) 20:22, 14 June 2020 (UTC)
One sentence reads as follows:
"The 5-cell has diploid pentachoric [3,3,3] symmetry,[7] of order 120, isomorphic to the permutations of five elements, because all pairs of vertices are related in the same way."
But isn't it necessary for — not just all pairs of vertices — but all vertices, as well as pairs, triples, and quadruples of vertices to be each related in the same way ... in order for the symmetry group to consist of all permutations of the vertices? 50.205.142.50 ( talk) 17:17, 26 June 2020 (UTC)
The following Wikimedia Commons files used on this page or its Wikidata item have been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 17:24, 23 August 2022 (UTC)