Timeline for Can we find lattice polyhedra with faces of area 1,2,3,...?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Jan 13 at 14:34 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
Added the 11-face golyhedron example
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Mar 17, 2017 at 10:13 | history | edited | CommunityBot |
replaced http://meta.mathoverflow.net/ with https://meta.mathoverflow.net/
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| Mar 9, 2016 at 22:58 | comment | added | Gerry Myerson | Nigin went on to find an 11-face golyhedron, yadi.sk/d/Zzw_Q6gKTZjwk | |
| Mar 9, 2016 at 18:18 | answer | added | Vigod | timeline score: 8 | |
| Jun 9, 2014 at 11:26 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Linked to Nigin's 15-face example. And now 12-faces.
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| Apr 30, 2014 at 0:16 | vote | accept | Joseph O'Rourke | ||
| Apr 30, 2014 at 0:16 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Addendum re Adam's solution; and Q3a.
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| Apr 29, 2014 at 17:48 | answer | added | Adam P. Goucher | timeline score: 47 | |
| Apr 28, 2014 at 16:09 | comment | added | The Masked Avenger | Actually "opposite corners" won't work: more care is needed. | |
| Apr 28, 2014 at 16:00 | comment | added | The Masked Avenger | @ChristianRemling, one way is to divide 1 through 4k into four sets of k members, with two set representing horizontal edge lengths and the other two vertical, with matching sums. I get (in clockwise order) 78216534 as a closed polygon for k=2. I imagine many k will yield solutions, by breaking a k solution in half and taking care to add 4 edges "at opposite corners". | |
| Apr 28, 2014 at 15:43 | comment | added | The Masked Avenger | With some tinkering I get 1123456789 (10 faces, with 12 adjacent, on up to 91 adjacent).(Oops. 56 are not adjacent.) | |
| Apr 28, 2014 at 1:43 | comment | added | Christian Remling | @JosephO'Rourke: Yes, thanks, that's what I had in mind. | |
| Apr 28, 2014 at 1:17 | comment | added | Joseph O'Rourke | @ChristianRemling: If I understand your meaning of "the 2 dimensional version," those are golygons: lattice polygons with edge lengths 1,2,3,... | |
| Apr 28, 2014 at 1:13 | comment | added | Christian Remling | Is the situation for the $2$ dimensional version of the question clear? Otherwise, this might be a good warm-up. | |
| Apr 28, 2014 at 0:46 | comment | added | Joseph O'Rourke | @QiaochuYuan: I take your fine suggestion! | |
| Apr 28, 2014 at 0:45 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
edited title
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| Apr 28, 2014 at 0:41 | comment | added | Qiaochu Yuan | If you don't mind some comments on possible reasons why this question might not have received the attention you wanted, the title is simultaneously forbiddingly wordy and does not really convey the spirit of the question. Perhaps a friendlier title like "Can we find polyhedra with faces of area $1, 2, 3, ...$?" might be better? | |
| Apr 28, 2014 at 0:36 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |