Timeline for Optimal 8-vertex isoperimetric polyhedron?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 6 at 19:52 | history | undeleted | Stefan Kohl♦ | ||
| Sep 6 at 19:52 | history | deleted | Stefan Kohl♦ | via Vote | |
| Apr 20, 2013 at 16:57 | comment | added | Henry Cohn | @joriki: That's great! | |
| Apr 20, 2013 at 12:38 | comment | added | joriki | I proved your assertion about the 5-vertex case in this math.SE post: math.stackexchange.com/questions/367287. | |
| Sep 8, 2011 at 19:10 | vote | accept | Joseph O'Rourke | ||
| Aug 30, 2011 at 4:06 | comment | added | Henry Cohn | By the way, someone should carry out a serious numerical investigation of isoperimetric problems for polytopes with a fixed number of vertices (if it hasn't already been done). I don't currently have the time or energy to do this right, but if anyone would like to try, I'd be happy to give them my crude code and some suggestions for how to do it better. Just send me an e-mail. | |
| Aug 30, 2011 at 3:57 | comment | added | Henry Cohn | Unfortunately, there's not much reasoning behind it: I wrote a program to optimize the isoperimetric ratio and ran it a bunch of times. I designed it for ease of programming rather than execution speed, so I couldn't gather a lot of evidence, but it found this configuration a number of times and never beat it (sometimes it got stuck in local optima). The program produced ugly coordinates but I played around with them and identified the structure described above. Given the three-parameter family, it's not hard to get 500 digits of accuracy, but that's not enough to identify the exact values. | |
| Aug 29, 2011 at 23:57 | comment | added | Joseph O'Rourke | Wonderful, Henry!! I hope I interpreted your construction correctly in the figure I posted. Do you care to adumbrate the skeleton of your reasoning? Seems like it might be close to a proof... | |
| Aug 29, 2011 at 5:14 | history | answered | Henry Cohn | CC BY-SA 3.0 |