Talk:Crystallographic point group

Crystal class used to redirect to Crystal system. This was incorrect, so I changed it to redirect here, which I believe is more appropriate. Although there may be nuances here which I'm not certain about. Refs:

• http://ruby.colorado.edu/~smyth/G30102.html
• http://www.iucr.org/iucr-top/comm/cteach/pamphlets/22/node22.html

There seems to be better information on point groups on the Crystal system page? I dont know enough to fix the problem.. can someone who knows their stuff please fix it. 60.234.48.118 23:57, 14 March 2007 (UTC)

O. Prytz 18:09, 8 January 2006 (UTC)

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:46, 10 November 2007 (UTC)

There is no explanation of the subscript 'd' placed after certain point groups of D, for example in D_2d. Also, under the discussion of possible subscripts for D, it mentions a possible v subscript, when that never seems to be used. Am i right in thiking that 'd' basically takes the desciption given to 'v'. If so could someone who fully understands why 'd' is used instead of 'v' provide an explanation. Thanks. —Preceding unsigned comment added by 129.31.240.38 (talk) 14:49, 30 May 2010 (UTC)

The expression is confusing. I don't think "Th is T with the addition of an inversion." Inversion? Maybe mirror plane? --Makecat_Talk 04:03, 30 January 2012 (UTC)

What's the mathematical definition of a point group? It would be nice for this page to include that. This is not a mathematical definition:

: a crystallographic point group is a set of symmetry operations, like rotations or reflections, that leave a central point fixed while moving other directions and faces of the crystal to the positions of features of the same kind.

Is a point group just a discrete subgroup of O(3), the group of rotations and reflections in 3 dimensions? No, because then the symmetry group of a dodecahedron would be a point group. Is it a discrete subgroup of O(3) that preserves some lattice? I'm not sure. Furthermore: when do two point groups count as "the same"? When they're conjugate in O(3)? Someone must know the answers. Not me. John Baez (talk) 08:08, 23 July 2016 (UTC)2602:306:80E8:2170:8C7C:C39B:5B19:DEA3 (talk) 17:37, 25 June 2017 (UTC)

I believe a point group is just any subgroup of O(3), so called because the entire group leaves a single point unchanged, as opposed to the space groups which include more general affine transformations. But this page is specifically about crystallographic point groups, i.e. ones consistent with Bravais lattices, which forces them to be finite groups with no operations beyond 1-, 2-, 3-, 4-, and 6-fold rotations and rotinversions. Two groups are the same if their sets of operations are identical to within a single overall coordinate transformation, itself an element of SO(3). There's probably an elegant and less confusing way of stating that.

I find this page useful as a reference for the maps among the different notations, and especially for the image showing the subgroup relationships. However, that image appears to have an error: If I'm not mistaken, 6mm is a supergroup of 3m, not 3bar.

BW Reed 2602:306:80E8:2170:8C7C:C39B:5B19:DEA3 (talk) 17:37, 25 June 2017 (UTC)

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In section "The correspondence between different notations", Cs is not explained anywhere. From context, I assume it is the group generated by one horizontal reflection only?

Also V is not linked or explained. Perhaps link to Klein_four-group#Geometry and edit that article to identify the the geometric representations D2, C2h = D1d, C2v = D1h with V, Vd, Vh, respectively, if this is the accepted notation?

Not sure enough to edit it myself... Chris2crawford (talk) 01:32, 11 September 2020 (UTC)

Maybe adding a few pictures for the symmetry groups could help understand the concepts better? Ash Psychic (talk) 06:02, 13 February 2025 (UTC)