I resend this mail, as there was obviously technical problems during sending
the original message. Best regards, Rudolf Zlabinger
----- Original Message -----
From: "Rudolf Zlabinger" <[EMAIL PROTECTED]>
To: "Walter Becker" <[EMAIL PROTECTED]>
Cc: "GAP Forum" <[EMAIL PROTECTED]>
Sent: Wednesday, August 02, 2006 5:55 PM
Subject: Re: icoshhedral group items maybe of interest?
Dear Walter Becker,
I dealt with fullerene rotations as an exercise for regular permutation
groups. In this case this is the regular permutation group for the
icosahedral group A_5. The rotations of the 60 vertex fullerene is the
regular permuation group of A_5. The remaining problem was, how to label
the
vertices according to the distinct permutation group used. I used the GAP
package GRAPE to construct a graph containing the adjacency matrix
showing,
how to label these vertices.
The remaining symmetries mentioned by you should be translations, i think,
i
didnt deal with yet.
I send you a log of a GAP session showing, how to proceed.
Thank you for your information, best regards, Rudolf Zlabinger
----- Original Message -----
From: "Walter Becker" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>
Sent: Wednesday, August 02, 2006 3:35 PM
Subject: icoshhedral group items maybe of interest?
Dear Drs Zlabinger and McKay:
I ran across the following article on the icosahedral group that may be
of interest. It was something I was interested in getting ---it contains
the symmetry adapted functions which one uses in allied work ---in ths
case dealing with the fullerene vibratonal studies of the C_(60)
mnolecule.
Aticle appears in Spectroscopy Letters volume 21 issue 4 pp319-339
(1988).
there is a previous article dealing with the fullerenes in the same issue
(the previous article).
Abstract of the article reads
A complete set of the 174 symmetry coordinates for teh C_(60) molecular
model referred to as footballene is reported. The model is the truncated
icosahedron (symmetry I_h). Hence in addition to triple degenmeracy also
quadruple and qunituple degeneracies occur.
Note the other 6 symmety functions here correspond to translations and
center of mass rotations of the whole molecule ---hence total of 60 time
3
or 180 total symmety adapted functions.
Hoe this is not old information
Walter Becker
gap> a5:=AlternatingSubgroup(SymmetricGroup(5));;
gap> a5_60:=RegularActionHomomorphism(a5);;
gap> a5_60_home:=last;
<action epimorphism>
gap> a5_60:=Image(a5_60_home);; # group acting on the 60 vertices of fullerene
isomorphic to the
gap> # icosahedron group A5
gap> # we want to draw now the graph containing the vertex adjacency matrix
gap> # in order to label the fullerene according to the group a5_60 found above
gap> fullerene:=EdgeOrbitsGraph(a5_60,[[1,2],[1,3],[1,4]]);;
gap> Adjacency(fullerene,1);
[ 2, 3, 4 ]
gap> Adjacency(fullerene,60);
[ 57, 58, 59 ]
gap> # the full adjacency matrix can also be drawn by:
gap> CollapsedAdjacencyMat(Group(()),fullerene);;
gap> quit;
_______________________________________________
Forum mailing list
[email protected]
http://mail.gap-system.org/mailman/listinfo/forum
