This article is ratedStart-class on Wikipedia'scontent assessment scale. It is of interest to the followingWikiProjects:

MathematicsLow‑priority This article is within the scope ofWikiProject Mathematics, a collaborative effort to improve the coverage ofmathematics on Wikipedia. If you would like to participate, please visit the project page, where you can jointhe discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics Low This article has been rated asLow-priority on theproject's priority scale. PolyhedraLow‑importance This article is within the scope ofWikiProject Polyhedra, a collaborative effort to improve the coverage ofpolygons,polyhedra, and otherpolytopes on Wikipedia. If you would like to participate, please visit the project page, where you can jointhe discussion and see a list of open tasks.PolyhedraWikipedia:WikiProject PolyhedraTemplate:WikiProject PolyhedraPolyhedra Low This article has been rated asLow-importance on theproject's importance scale.

An octahedron has 12 edges, so there cannot be four pairs of opposite edges. Isn't S_4 acting on opposite FACES?

139.104.180.28 (talk)02:00, 27 September 2017 (UTC)[reply]

That sounds more likelyWoscafrench (talk)16:36, 27 September 2017 (UTC)[reply]

I added the cleanup tag because this article needs more work. I like the examples added at the end, but they should be cleaned up, and data tables (pasted from elsewhere) removed as redundant.

Well, not necessarily a lot of work, but more than I want to do tonight!

Tom Ruen09:21, 22 February 2006 (UTC)[reply]

Please do not remove data tables, it is convenient to have data about examples together on this page.--Patrick12:35, 22 February 2006 (UTC)[reply]

Hey,Patrick, what do you think about cleaning up the formatting here? Is it really necessary to have cut&pasted tables here from elsewhere?

Tom Ruen07:22, 25 February 2006 (UTC)[reply]

I do not see tables from elsewhere, just selected parts regarding the subject of the article.--Patrick12:44, 25 February 2006 (UTC)[reply]

I propose that the article be moved tocubical symmetry, which seems to me (based on experience) to be the more common name. A redirect fromoctahedral symmetry would be right.Zaslav01:58, 16 November 2006 (UTC)[reply]

The name comes from symmetry terminology. See this framework: (Note - I'm not defending the quality or contents, merely the terminology!)

1. List of spherical symmetry groups
2. dihedral symmetry - Dn, Dnh, Dnd
3. tetrahedral symmetry - T, Td, Th
4. octahedral symmetry - O, Oh
5. icosahedral symmetry - I, Ih

I added the Stub tag at the bottom of the page, although the cleanup tag makes it redundant. Another Redundancy! —The Doctahedron,68.173.113.106 (talk)22:21, 24 November 2011 (UTC)[reply]

Does a polyhedron exist that has octahedral and icosahedral symmetry groups and is flag-transitive????? —The Doctahedron (talk)22:29, 24 November 2011 (UTC)[reply]

Not a convex polyhedron. (The only flag-transitive convex polyhedra are the platonic solids.) And not a star polyhedron either. Nor skew polyhedra, which are infinite. You would have to look at abstract 3-polytopes for any possibilities. --kundor (talk)16:19, 25 October 2013 (UTC)[reply]

It is written in the text that Octahedral symmetry contains C3h symmetry - this is not true !— Precedingunsigned comment added by195.176.182.224 (talk)08:23, 21 May 2012 (UTC)[reply]

Good catch. —Tamfang (talk)18:58, 21 May 2012 (UTC)[reply]

Here's my reproduction of Conway's subgroup presentation, from The Symmetries of things, p280. It's more organized than an explicit tree, and contains some multiple copies of subgroups based on different relations. Conway showed + groups, - groups, and one middle +/- group, which I show as yellow/green, and pink respectively. I also drew red horizontal lines showing the group order divisions. The green lines show order-3 subgroup relationships between upper-left and lower-right graphs.Tom Ruen (talk) 05:17, 14 December 2013 (UTC) I added a second graph, showing the symmetries on a truncated cuboctahedron, flattening rows to constant index, and suppressing all subgroup relation lines.Tom Ruen (talk)03:39, 15 December 2013 (UTC)[reply]

Conway's subgroup tree

Subsymmetries ontruncated cuboctahedron

I found the phrase "symmetry order" in the introductory paragraph. This is a phrase that virtually no mathematician or math student has ever heard.Therefore do not use it.

The next section,Details, is almost 100% incomprehensible from the first word.

Suggestion: If you have no idea whatsoever how to communicate mathematics, please don't do it in Wikipedia.2600:1700:E1C0:F340:50EC:9DF9:703F:5234 (talk)00:50, 9 July 2019 (UTC)[reply]

• Start-Class mathematics articles
• Low-priority mathematics articles
• Start-Class Polyhedra articles
• Low-importance Polyhedra articles