One can do something like this; start from your graph G, take D=G.planar_dual(), in D take a spanning tree, and starting from the root of the tree, and orientation chosen in the face corresponding to the root, proceed recursively to induce orientations on the adjacent faces.
On Mon, Jun 19, 2023 at 2:00 PM Dima Pasechnik <dimp...@gmail.com> wrote: > > oh, right, what I suggested isn't what you asked for, sorry. > > > On Mon, 19 Jun 2023, 13:56 John Cremona, <john.crem...@gmail.com> wrote: >> >> Thanks Dima for the suggestion. I'm not sure that this does what I need: >> the associated directed graph has each edge directed, which is not what I >> was needing, and the faces of the directed graph look identical to those of >> the original -- in particular, the edges of each face are tuples (x,y) where >> both (x,y) and (y,x) appear on different faces (as I need to always hold) >> regardless of the orientation of the edges. >> >> I will keep on experimenting. My polyhedra are small and few enough that >> check the orientations of each is not very time-consuming. >> >> John >> >> On Monday, June 19, 2023 at 12:08:18 PM UTC+1 Dima Pasechnik wrote: >>> >>> On Mon, Jun 19, 2023 at 11:18 AM John Cremona <john.c...@gmail.com> wrote: >>> > >>> > I have some quite small graphs which are polyhedral, each is the >>> > 1-skeleton of a (connected convex) polyhedron such as a cube, >>> > tetrahedron, etc, constructed from a list of edge pairs. >>> > >>> > I can get the faces of one of these, say G, via G.faces(). This returns a >>> > list of lists of vertices, each one being a list of the vertices of one >>> > face in some cyclic order. So each face in the list has an implied >>> > orientation. OK so far. >>> > >>> > What I want is for the orientations of the different faces to be >>> > coherent, coming from a single orientation of the surface. Expliticly >>> > that means that each edge xy, which will appear in exactly two faces, >>> > appears once in each direction, i.e. x before y (cyclically) in one and >>> > the other way round in the other. >>> > >>> > It is possible that G.faces() is already returning such a globally >>> > oriented list of faces, as experimentation suggests, but I need to be >>> > certain -- otherwise I can write code to check and if necessary reverse >>> > some faces. I would prefer not to have to though. >>> > >>> > The docstrong of G.faces() does not make this clear (at least not to me). >>> >>> You can call G.strong_orientation() >>> to get an orientation of the edge of your graph, and use it. >>> >>> HTH >>> Dima >>> >>> > >>> > -- >>> > You received this message because you are subscribed to the Google Groups >>> > "sage-support" group. >>> > To unsubscribe from this group and stop receiving emails from it, send an >>> > email to sage-support...@googlegroups.com. >>> > To view this discussion on the web visit >>> > https://groups.google.com/d/msgid/sage-support/CAD0p0K5e9ch3tgrM2RAHxQieVOqG%2BEX37fyWj7BwF0ns-NTPpA%40mail.gmail.com. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-support" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sage-support+unsubscr...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-support/08ace3c1-1e96-427a-97a1-53605ca42742n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAAWYfq1Rd%2BOmDBLY9x4ZZFn99WFrGShS98%2BPc39zHfw4jcgZvA%40mail.gmail.com.
