Timeline for Is this an instance of any existing convex pentagonal tilings?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2015 at 11:49 | history | edited | Per Alexandersson | CC BY-SA 3.0 |
added 71 characters in body
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| Aug 25, 2015 at 11:47 | comment | added | Per Alexandersson | @YoavKallus: Ah, you are right! | |
| Aug 25, 2015 at 5:29 | comment | added | Yoav Kallus | Jacky's tiling is not isohedral. Some pentagons have the long edge (the one between the two parallel edges) meeting a long edge, while some pentagons have the long edge meeting two short edges. Therefore, those two different pentagons cannot be equivalent. | |
| Aug 25, 2015 at 4:06 | comment | added | Noam D. Elkies | Again, Wikipedia does not answer quite the same question. The five Reinhardt classes of pentagons all have 1-isohedral tilings. Some of them may also have other 1-isohedral tilings. So the fact that Jacky's tiling is 1-isohedral doesn't force it to be either new or one of the five types of tilings shown, even though the pentagon does fall in at least one of Reinhardt's classes. | |
| Aug 25, 2015 at 3:34 | comment | added | Per Alexandersson | Added: According to this source, jaapsch.net/tilings/Tilings.pdf all 1-isohedral tilings are fully understood.... | |
| Aug 25, 2015 at 3:32 | comment | added | Per Alexandersson | Yeah, it seems so simple, that it is most likely in the original family of 5, since it has the 1-isohedral property, and these are probably easy to exhaust/verify is complete by computer search (but I might be completely wrong on this, maybe suitable as a follow-up question?). | |
| Aug 25, 2015 at 3:18 | comment | added | Jacky | Thanks. I guess by p4 you were referring to type 4? If you take a look at the 2nd generalization in my answer to my own question, you would find out that only 1 right angle is needed, while type 4 pentagon needs 2 right angle. As answered by Noam, it actually belongs to type 1 I guess, since type 1 pentagons summarizes all pentagons with parallel sides, which include both of my generalizations. | |
| Aug 25, 2015 at 3:10 | history | answered | Per Alexandersson | CC BY-SA 3.0 |