Timeline for Sphere - Symmetry and Triangulation [closed]
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2013 at 21:55 | comment | added | Wlodek Kuperberg | I do not understand why this question has been put on hold. I admit that it has been phrased somewhat ambiguously, but it has been clarified by the comments, and is related to some very hard questions on triangulating or tiling the sphere with small regions. The comments by Ian Agol (though he presumes the intentions of warsaga) and by j.c. (though his - or her - guess is not quite right) indicate their interest in the question, contrary to the reasons given for putting it on hold... | |
| Oct 9, 2013 at 19:52 | history | closed |
j.c. Andrey Rekalo David White Ryan Budney Benoît Kloeckner |
Not suitable for this site | |
| Oct 9, 2013 at 17:43 | answer | added | Joseph O'Rourke | timeline score: 2 | |
| Oct 9, 2013 at 17:32 | answer | added | Wlodek Kuperberg | timeline score: 4 | |
| Oct 9, 2013 at 14:37 | comment | added | Wlodek Kuperberg | @j.c.There are many more triangulations of $S^2$ with dihedral groups of symmetries than just bipyramids. The triangles could be arbitrarily small, arranged in several horizontal layers between the South and the North poles, the layers forming prisms or antiprisms, with two pyramids at the poles. | |
| Oct 7, 2013 at 10:44 | comment | added | warsaga | Could you write your comment as and answer an I will accept it. | |
| Oct 6, 2013 at 17:03 | review | Close votes | |||
| Oct 8, 2013 at 22:52 | |||||
| Oct 6, 2013 at 16:49 | comment | added | Ian Agol | As indicated by j.c., the finite subgroups of SO(3) have closure proper subgroups of SO(3) (the infinite dihedral group). So one cannot find a sequence of triangulations whose symmetry converges to a group containing every rotation as I think you would like. An analogous result holds for every dimensional sphere, essentially by the Zassenhaus lemma. | |
| Oct 6, 2013 at 16:43 | comment | added | j.c. | Well, the "largest" finite subgroups of $SO(3)$ are going to be dihedral groups, so I guess that means you'll be looking at bipyramids en.wikipedia.org/wiki/Bipyramid | |
| Oct 6, 2013 at 16:32 | comment | added | warsaga | Thank you. I am referring to all isometries of the sphere that preserve the triangulation. | |
| Oct 6, 2013 at 16:23 | history | edited | Ricardo Andrade |
edited tags
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| Oct 6, 2013 at 16:21 | comment | added | Ricardo Andrade | Dear @warsaga: What do you mean by a symmetry of the triangulation? Do you want to consider all automorphisms of the 2-dimensional simplicial complex associated with the triangulation? Or are you referring to isometries of the sphere which preserve the triangulation? | |
| Oct 6, 2013 at 16:12 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced deprecated tag 'geometry'; removed tag 'co.combinatorics' as it appears to not apply
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| Oct 6, 2013 at 16:04 | history | asked | warsaga | CC BY-SA 3.0 |