Talk:Tetrahedral symmetry

Cleanup (Feb 06)

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 Ruen 09:21, 22 February 2006 (UTC)

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 Ruen 07:21, 25 February 2006 (UTC)

Rude remark (March 06)

Apologies to whoever wrote this, but this page is terrible. An encyclopedia is supposed to explain something to someone who doesnt know about it. Anyone looking up this page would be totally confused. What is needed is just a simple picture of a tetrahedron at the top, a statement that there are 12 or 24 symmetries depending on whether you include reflections or not, and a mention of the group A_4. PCM

I agree, so I added a few sentences at the beginning doing just that. I think the rest of the article needs work but I'm not sure how to proceed on that. --Experiment123 00:21, 14 March 2006 (UTC)

I added the cleanup notice, and mostly because of the cluttered pictures, not willing to step into actual content!

Same issues for

1. octahedral symmetry
2. icosahedral symmetry

Tom Ruen 02:29, 14 March 2006 (UTC)

I added the same kind of intro to octahedral symmetry and icosahedral symmetry. Hope it helps! --Experiment123 03:38, 14 March 2006 (UTC)

Yep, this page is typical Patrick work. It is rude to say that, but I can see where he worked from a mile. Lots of incomprehinsible wording all around. Oleg Alexandrov (talk) 15:24, 14 July 2006 (UTC)

Looks like a good time for some revamping here. I added a subgroup tree as a starter, and added some tables. I have a [4,3] subgroup table with pyritohedral symmetry, so I'll made a smaller table for that here too File:Octahedral subgroup tree.png, possibly being a bit neater, but maybe someone else can remake in SVG. Oh, my proference is for Coxeter notation from n-dimensional uniform polytope work, but where helpful I'll support many notations, like summary here List_of_spherical_symmetry_groups. Tom Ruen (talk) 23:48, 10 May 2013 (UTC)

Wrong reference

In sentence It is the direct product of the normal subgroup of T (see above) with Ci. Ci links to Inversive geometry. It is wrong reference link. Must be Point reflection. Jumpow (talk) 21:16, 1 December 2015 (UTC)

Yes, looks like the wikilink isn't correct, whether it was at some point I don't know. I changed to point reflection as you suggested. Tom Ruen (talk) 23:00, 1 December 2015 (UTC)

Pyritohedral symmetry

Why is Pyritohedral symmetry a chapter in this article? I think it should be in Octahedral symmetry. T_h is a subgroup of O_h, but not of T_d. (See File:Full octahedral group; subgroups Hasse diagram.svg) Watchduck (quack) 23:53, 14 September 2018 (UTC)
@Tomruen: Do you think this should stay like this? Watchduck (quack) 00:21, 25 October 2018 (UTC)

It certainly is debatable in my mind, and strange when I first saw it. Can we find some sources to help? Schoenflies notation might explain the grouping as T, T_h, T_d, and strangely the h extension gives all reflectins for oct/ico, while pyrit for tet (because of lack of inversion symmetry apparently). So from my memory some source would seem to take the chiral symmetries as primary, and the reflective symmetries are doublings of those. So there are two extending symmetries of chiral tetrahedral, and one extending symmetry of chiral octahedral. Tom Ruen (talk) 04:56, 25 October 2018 (UTC)

Subgroups of A₄×C₂ as the pyritohedral group T_h or [3⁺,4]

The relationship between pyritohedral with chiral tetrahedral symmetry can be seen in the diagram on the right. (See also here.) This relationship certainly justifies mentioning T_h in the section about T..

Octahedral symmetry is already quite crowded. I think the best choice would be to give Pyritohedral symmetry its own article, and add a small section about it in tetrahedral, octahedral and icosahedral symmetry. Watchduck (quack) 00:00, 27 October 2018 (UTC)