tag:blogger.com,1999:blog-124350264510724511.post2165942146636277958..comments2024-01-15T16:21:42.238+02:00Comments on Unitary Flow: Polyhedra and GroupsCristi Stoicahttp://www.blogger.com/profile/00577217435388643300noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-124350264510724511.post-7427516616139565422014-03-17T09:40:59.704+02:002014-03-17T09:40:59.704+02:00Doug,
> The vertices of the dodecahedron can b...Doug,<br /><br />> The vertices of the dodecahedron can be assigned single digits and the edges assigned the permutation.<br /><br />I preferred to label the edges to be consistent with Klein's coloring, to use it also in that context.<br /><br />One can label each vertex of the dodecahedron by starting from the solution presented in the article. One can use for example the following rule: each vertex is labeled with the second digit which appears in all three permutations which meet in that vertex. This rule exploits the fact that all three permutations at the same vertex have the same number on the second position. The resulting group is $A_5$.<br /><br />> For 6 element permutations the polyhedron becomes instead a plane tiled with hexagons.<br /><br />Actually, the group $S_6$ is not a subgroup of the group of isometries of the plane. But you can obtain its subgroups of the form $Z_n$ and $D_n$, where $n$ divides $6$.Cristi Stoicahttps://www.blogger.com/profile/00577217435388643300noreply@blogger.comtag:blogger.com,1999:blog-124350264510724511.post-51570068006368760092014-03-16T23:20:27.637+02:002014-03-16T23:20:27.637+02:00Hello, and thank you for the interesting article. ...Hello, and thank you for the interesting article. The vertices of the dodecahedron can be assigned single digits and the edges assigned the permutation. This is consistent with your cube example and neater. For 6 element permutations the polyhedron becomes instead a plane tiled with hexagons. <br /><br />cheers,<br /><br />Doug Barrett<br />EdmontonAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-124350264510724511.post-20633549578270232072011-02-24T23:11:36.898+02:002011-02-24T23:11:36.898+02:00Hi Bernard,
you may find helpful
this online book...Hi Bernard,<br />you may find helpful <br /><a href="http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=03070001" rel="nofollow">this online book</a>.Cristi Stoicahttps://www.blogger.com/profile/00577217435388643300noreply@blogger.comtag:blogger.com,1999:blog-124350264510724511.post-91415890498368385882011-02-22T05:41:17.633+02:002011-02-22T05:41:17.633+02:00hi,im bernard and currently making a thesis paper ...hi,im bernard and currently making a thesis paper regarding the permutation of the platonic solids,did the formed cycles from the permutation is disjoint?and how is it related to the ruffini's theorem?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-124350264510724511.post-72920231257004322622009-12-04T11:48:52.909+02:002009-12-04T11:48:52.909+02:00Thank you.
The way I used polyhedra to represent ...Thank you.<br /><br />The way I used polyhedra to represent group multiplication was the result of my own work. The ideas come to me when I studied group representations and the symmetry groups of regular polyhedra. I created the models several years ago on the computer and out of carton.Cristi Stoicahttps://www.blogger.com/profile/00577217435388643300noreply@blogger.comtag:blogger.com,1999:blog-124350264510724511.post-57245092792179886082009-12-02T13:58:30.717+02:002009-12-02T13:58:30.717+02:00hi, very good exposition. can you please tell me w...hi, very good exposition. can you please tell me where you gathered the material from ? a bibliography ? also, did you actually create the polyhedra yourself out of cartonboard or paper to visualize this ? thanksAnonymousnoreply@blogger.com