Closed CunningGabe closed 2 years ago
Do we want this for non-reflexible maniplexes? We talked only about regular polytopes, but maybe this can be generalized at least to chiral?
Yeah, I guess it makes sense for chiral - we can still ask whether the group automorphism that sends each si to s{n-i}^-1 is inner or outer. So let's just do it for chiral and reflexible for now.
Sounds good. I will add this tomorrow.
Do we have the ability to grab the standard generators s_i if you are given a chiral maniplex?
Normal AutomorphismGroup(M) won't give the appropriate gens.
It depends on how the chiral maniplex was built - for example, anything built from RotaryManiplex should give those generators, but random maniplexes that are later discovered to be chiral will not.
For example, compare AutomorphismGroup(ToroidalMap44([1,2])) with AutomorphismGroup(ToroidalMap44([1,2],[-2,1])).
It shouldn't be hard to make AutomorphismGroup try to put the group of a chiral maniplex in a standard form. I'll add an issue for that.
IsInternallySelfDual( M[, x] ) is done for the reflexible case, and is ready to go for chiral once the automorphism groups are well behaved.
Done for chiral in 3c232bcecb2cc33737563b77dbb25aae1ddada7e.
c.f. my paper with Mark.
(Not to be confused with proper and improper self-duality, which is different)