Talk:Point groups in three dimensions

Merge

I think it would be a good idea to merge this article into the one on point groups. I don't really see that we need a separate aricle for the 3D case. We also have an article on Crystallographic point groups that deals specifically with point groups in crystallography (which i think is ok). So there's in total 3 articles relating to different cases of point groups, which makes it pretty confusing to anyone not familiar with the subject. O. Prytz 00:00, 6 June 2006 (UTC)

I agree, I think the central article should be at point groups too. --HappyCamper 02:40, 18 August 2006 (UTC)

I do not agree. We have also Point groups in two dimensions. Point group is an introduction for general dimension.--Patrick 08:42, 7 October 2006 (UTC)

Point groups are already quite full. Maybe something from there should come here. Point groups in four dimensions might be the next case for a separate article.--GuenterRote (talk) 20:39, 29 January 2013 (UTC)

I disagree. The 3-dimensional case is easier to grasp and is more widely applicable. It is very useful to have an article focused on it, without distraction from generalizations. 188.154.206.128 (talk) 21:09, 13 January 2019 (UTC)

Merge Polyhedral groups

That article is almost empty and should go to this article: Point groups in three dimensions--GuenterRote (talk) 20:39, 29 January 2013 (UTC)

sub/super

How about a table something like this:

		immediate subgroups	immediate supergroups
Ih	120	I, Th, D5d, D3d	—
I	60	T, D5, D3	Ih
Oh	48	Td, Th, D4h, D4d, D3d	—
O	24	T, D4, D3	Oh
Td	24	T, D2d, C3v	Oh
Th	24	T, D2h, S6	Oh, Ih
T	12	D2, C3	Td, Th, O, I
Dnh	4n	Dn, Cnh	Dmnh
Dnd	4n	Dn, Cnv, S2n	Dmnd

and so on. —Tamfang 01:07, 9 May 2007 (UTC)

Sure, that seems like a reasonable and useful summary of the various relationships among the groups.

Also in that spirit, how about a table of irreducible representations of some common groups for spectroscopic applications, a la F.A. Cotton? Baccyak4H (Yak!) 01:54, 9 May 2007 (UTC)

fixed point

There's a sentence in the second paragraph that is incorrect.

"All isometries of a bounded 3D object have one or more common fixed points."

Take a solid torus and rotate about its plane. I suppose it is meant: They have a fixed point in R^3. —Preceding unsigned comment added by 18.87.1.204 (talk) 16:59, 6 September 2008 (UTC)

Or invert it in the center. Since this is an article about point groups, we can take the fixity of the origin as implied, and it's clearly false that all isometries must have another fixed point. —Tamfang (talk) 07:39, 12 September 2008 (UTC)

Name for infinite families, relation to frieze groups

I think that we should work this into the article somehow.

Taken from this paper: [1] Three-dimensional finite point groups and the symmetry of beaded beads, G.L. Fisher and B. Mellor, Journal for Mathematics and the Arts, Vol. X, No. X, Month 2007

The 7 infinite families F&M call the prismatic groups, after their being the symmetry groups of n-sided right regular prisms. The remaining 7 groups F&M call the Platonic groups, after their association with the Platonic solids.

In their paper, they note relationships between the families and the [frieze group]s. I'll list: Schoenflies symbol, orbifold symbol, F&M's symbol, IUCr symbol, and number in the Wikipedia article. I'll represent the frieze groups with ASCII art for convenience.

C(n) - nn - 11 - p1 - #1

b b b b b

C(n,h) - n* - 1m - p11m - #3

b b b b b
p p p p p 

C(n,v) - *nn - m1 - p1m1 - #4

bdbdbdbdbd

D(n) - 22n - 12 - p211 - #5

b b b b b
 q q q q q

S(n) - nx - 1g - p11g - #2

b b b b b
 p p p p p

D(n,d) - 2*n - mg - p2mg - #6

bdbdbdbdbd
qpqpqpqpqp

D(n,h) - *22n - mm - p2mm - #7

bdbdbdbdbd
pqpqpqpqpq

The prismatic groups and the frieze groups share orbifold symbols, but with n = infinity for the frieze groups.

The IUCr symbols are in Hermann–Mauguin notation, and they are from (from [2] Fundamentals of Crystallographic Symmetry by Paolo G. Radaelli, and SpringerLink: The 7 frieze groups

Lpetrich (talk) 23:00, 16 June 2011 (UTC)

another merge

What is in List of spherical symmetry groups that isn't duplicated here? —Tamfang (talk) 23:23, 30 October 2012 (UTC)

Yes, I added it there too, as a shorter summary article. The table I added is a summary of the second text, although I like including the different notations. It could be removed here, if the prose are enough. I added the 2D wallpaper groups also List_of_planar_symmetry_groups#Rotation_subgroups, while there's no equivalent content at wallpaper group. SockPuppetForTomruen (talk) 00:01, 31 October 2012 (UTC)

Unclear sentence

There are four C3 axes, each through two vertices of a cube (body diagonals) or one of a regular tetrahedron, ...

What is one of here? It cannot be two vertices of tetrahedron. It cannot be one of two tetrahedrons.

But than what is it? Jumpow (talk) 08:23, 30 April 2017 (UTC)

Each axis passes through one face and one opposite vertex of the tetrahedron. (or through pairs of opposite vertices of a cube) Tom Ruen (talk) 08:28, 30 April 2017 (UTC)

Thank you. Now I understood. Another question, what is squared norm. Is it Euclidean norm? Jumpow (talk) 09:01, 30 April 2017 (UTC)

PS: Excuse me, I sometimes ask, may be, obvious questions. I translate articles to Russian, and if I do not understand sentence exactly, I stop and cannot go forward. Jumpow (talk) 09:10, 30 April 2017 (UTC)

I'm not sure what it means in this context. It was added in 2013 by User:Eric Kvaalen. - Tom Ruen (talk) 09:19, 30 April 2017 (UTC)

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