Timeline for Which unfoldings of the hypercube tile 3-space: How to check for isometric space-fillers?
Current License: CC BY-SA 3.0
13 events
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| May 16, 2021 at 16:58 | comment | added | Joseph O'Rourke | @Dirk: A natural question, also asked in my paper with a student. The answer is unknown, but no counterexample has been found. I'm inclined to guess: Yes for all $261$ unfoldings. | |
| May 16, 2021 at 16:21 | comment | added | Dirk | Do the unfoldings of the unfoldings of a 4-cube tile 2-space? | |
| May 15, 2021 at 22:15 | vote | accept | Joseph O'Rourke | ||
| May 15, 2021 at 8:50 | answer | added | Moritz Firsching | timeline score: 40 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Dec 8, 2015 at 11:16 | comment | added | Joseph O'Rourke | @StevenStadnicki: Thanks! Indeed, that is the next natural question, and it is posed as the 3rd open problem on p.19. | |
| Dec 8, 2015 at 6:10 | comment | added | Steven Stadnicki | The note looks fantastic - I really like your Dali tiling. With several of the unfoldings confirmed to tile, I suppose the next natural question is 'have any been confirmed to not tile space?'... | |
| Dec 8, 2015 at 2:26 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Mar 7, 2015 at 21:43 | answer | added | Joseph O'Rourke | timeline score: 8 | |
| Mar 5, 2015 at 13:06 | comment | added | Mark McClure | I wondered about your motivation! The second tiling that is illustrated in that video shows that there is a natural approach to generating the tiling, when the tree associated with the unfolding is the path on 6 vertices. There are four such unfoldings of the cube into the plane. Of the 261 unfoldings of the tesseract into space, there are 24 whose associated tree is the path graph on 8 vertices. I wonder if a similar approach would yield tilings of space by these? Presumably, a visualization of the unfolding process would help determine this - something I was considering working on next week. | |
| Mar 5, 2015 at 7:08 | answer | added | Steven Stadnicki | timeline score: 5 | |
| Mar 5, 2015 at 0:18 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
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| Mar 5, 2015 at 0:06 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |