> " Although only 2 permutations are needed for a polyhedron in order to > generate all the possible orientations, it is customary to give a > group of permutations (P0, P1, ...) such that powers of them alone are > able to generate the orientations, e.g. P0, P0**2, P0**3, P1, P1**2, > etc..., instead of mixed permutations (P0*P1**2*P0). The following > work was used to calculate the permutation group of the polyhedra." > > What does this mean? Why is it customary to give a "group" (you > mean "set" or "collection" I guess?) of perms s.t. powers alone generate > the "orientations" (I guess you mean "group elements" I guess?)? > I don't understand what this means.
One can supply a "pgroup" to Polyhedron so I was using the word "group" for that purpose. I'm open to a new way of saying this. For a cube you could generate all permutations with two permutations: one that corresponds to rotating cw from the top and one that corresponds to rotating cw from the front face. But there are 3 face, 6 edge and 4 vertex permutation groups that can be defined, too. Multiple applications of just the top and front face will not show you all orientations of the cube -- they can only show you 6 of the 24 -- whereas application of the others will show all the orientations. I don't know how best to say this. > > I was also confused at first what "0-based" and "1-based" cycle notation > meant. I figured it out (or think I did) from the context and your examples, > but others might find it confusing. Just FYI. I think a way around this is to always add 0 to permutations that don't have a 0 and just let the user ignore that 0. That way they can give permutations with or without the zero and those functions for dealing with one or the other can be removed. > > Second, you say you give tests but no where do I see you say > "the permutation group representation of the symmetry group > of the cube is isomorphic to S_4" and test that the group you > generate has 24 elements. Am I missing something? The check() function in test_polyhedron does this. For each type of polyhedra it checks that 24 different orientations are generated. It also makes sure that each permutation given cycle back to the original within the allowed number of applications. > Similarly, I did not see "the permutation group representation > of the symmetry group of the dodecahedron is isomrphic to A_5" > and test that it has 60 elements. > If you don't do this, I don't see how you can be sure it is correct. I sweated over this for a couple of days...and got it wrong several times! :-) I think the test is correct but it would help if you took a look to see if it's convincing to you. Also, if there is a more correct way of saying something, please just annotate the code in github and I can see exactly the line you are referring to and can make the change. Thanks for looking this over. I'll keep working out the kinks related to multiplication order. /c -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
