I have constructed a combinatorial polytope, by specifying VERTICES_IN_FACETS. I would like to know the size of the combinatorial automorphism group (that is, the automorphisms of the face lattice.) Is there some way to determine this?
Thanks.
So lets walk you through an example. Let us take just the combinatorial information of the 3-cube and plug it into the client:automorphisms(m) -> Array<Pair<Array<Int>,Array<Int>>>
Find the automorphism group of the non-symmetric incidence matrix.
Arguments:
IncidenceMatrix<NonSymmetric> m
Returns Array<Pair<Array<Int>,Array<Int>>> each element encodes a permutation of its rows (first) and columns (second).
Code: Select all
polytope > $gen = automorphisms(cube(3)->VERTICES_IN_FACETS);
polytope > print $gen;
(<0 1 4 5 2 3> <0 1 4 5 2 3 6 7>)
(<2 3 0 1 4 5> <0 2 1 3 4 6 5 7>)
(<1 0 2 3 4 5> <1 0 3 2 5 4 7 6>)
Code: Select all
polytope > $genarray = [map {$_->[1]} @$gen];
polytope > $G = new group::Group(GENERATORS=>$genarray);
Code: Select all
polytope > print $G->ORDER;
48