[GAP Forum] Group Actions In GAP

[Michele Nardella]

Dear Subscribers to the GAP Forum,

I am an undergraduate student and taking my first class in Group Theory.
I would like to obtain
a) the permutation cycles of the faces of a truncated octahedron induced by
the action of its rotation group (S_4); and
b) the orbits of its faces;

To generate S_4 in GAP is the easiest part.
By I do not know, how to specify the domain, \Omega, and \mu which is
defined to be "a  function compatible with the group arithmetic." (
http://www.gap-system.org/Manuals/doc/ref/chap41.html).

Since a truncated octahedron  is made of 8 regular hexagons and 6 squares,
would I be correct in specifying the domain as
gap>dom:=[[1,2,3,4,5,6,7,8],[9,10,11,12,13,14]];
where 1..8 are the labels of the hexagonal faces and 9..14 are the label of
the squared faces?

Concerning the method \mu, GAP manual specifies many different options
ranging from paragraph 41.2-1 to 41.2-15. I have no idea which one apply to
my case.
Would you be so kind to give to me an hint?
Moreover, I will really appreciate if you can suggest to me some reference
so that I can understand a good portion of the other methods with the
constraint that I am an undergraduate student

Thank you very much,

Michele