Timeline for Why do convex polytope options constrict with dimension, rather than expand?
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 18, 2013 at 16:23 | vote | accept | Joseph O'Rourke | ||
| Nov 18, 2013 at 6:34 | answer | added | Igor Pak | timeline score: 14 | |
| Nov 18, 2013 at 2:46 | comment | added | Will Jagy | math.ucr.edu/home/baez/octonions/integers/integers_4.html | |
| Nov 18, 2013 at 1:18 | comment | added | Qiaochu Yuan | A rough estimate of the number of constraints is that an $n$-simplex has $n!$ flags, and regularity means that the symmetry group acts transitively on flags. | |
| Nov 18, 2013 at 1:16 | comment | added | Joseph O'Rourke | Excellent point, @QiaochuYuan! I wonder if that intuition can be made more precise, that constraints outrun freedom...? | |
| Nov 18, 2013 at 1:14 | comment | added | Qiaochu Yuan | "Regular" seems like a more important adjective than "convex" in the title. Anyway, my intuition is that while the amount of room might increase, it doesn't increase as quickly as the number of constraints imposed by regularity. Graph embeddings, on the other hand, don't have to have any kind of symmetry properties. | |
| Nov 18, 2013 at 1:12 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Clarifying (hopefully).
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| Nov 18, 2013 at 1:09 | comment | added | Will Jagy | Meanwhile, our own Jim Humphreys has a book math.umass.edu/~jeh/pub/book.html on Coxeter groups and reflection groups that probably gives a complete answer. | |
| Nov 18, 2013 at 1:01 | comment | added | Will Jagy | I like Coxeter's book, Regular Polytopes. He wasn't just a pretty face. | |
| Nov 18, 2013 at 0:55 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |