Timeline for 3D models of the unfoldings of the hypercube?
Current License: CC BY-SA 3.0
19 events
when toggle format | what | by | license | comment | |
---|---|---|---|---|---|
May 9, 2022 at 9:46 | comment | added | Joseph O'Rourke | @JeppeStigNielsen: See Number of hypercube unfoldings. | |
May 9, 2022 at 7:27 | comment | added | Jeppe Stig Nielsen | Oh, so we have a sequence 1, 11, 261, ... | |
Jul 15, 2019 at 1:57 | comment | added | Glen Whitney | Re the number of free octacubes: en.wikipedia.org/wiki/Polycube says it is 3811. So really it is quite unlikely for an octacube to be a net of a hypercube. | |
May 23, 2018 at 18:44 | comment | added | Menachem | I notice that of the 11 unfoldings of the cube, 2 have mirror symmetries and the other 9 do not. If we count the "chiral" pairs separately, then we have a total of 20 unfoldings. From the beautiful figures in two of the answers, it is difficult for me to tell how many of the 261 unfoldings of the 4D hypercube have mirror symmetries. Does someone know? | |
May 21, 2018 at 11:04 | answer | added | Moritz Firsching | timeline score: 15 | |
Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
Mar 17, 2015 at 13:46 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Link to followup question.
|
Mar 4, 2015 at 1:51 | vote | accept | Joseph O'Rourke | ||
Mar 4, 2015 at 1:48 | answer | added | Mark McClure | timeline score: 25 | |
Mar 1, 2015 at 14:36 | comment | added | Joseph O'Rourke | @ManfredWeis: That is a legitimate question, but I would prefer not to answer it. | |
Mar 1, 2015 at 12:33 | comment | added | Joseph O'Rourke | @TheMaskedAvenger: Oh, I see. There are 369 planar "free" octominoes. Haven't yet found a count in 3D. | |
Mar 1, 2015 at 6:48 | comment | added | The Masked Avenger | octominoes are like pentominoes, but composed of 8 squares instead of five. I'm suggesting that connected arrangements of 8 cubes are not much more numerous than unfoldings of a tesseract. But I don't know. | |
Mar 1, 2015 at 5:34 | comment | added | Noam D. Elkies | "Domino's Sugar? I'd like to place an order for $2088$ sugar cubes..." | |
Mar 1, 2015 at 4:14 | comment | added | Manfred Weis | @Joseph: what would be the benefit of having such models? Along with additional information, like the properties of the cube's face-adjacency graph or usability in architecture, a complete set of such 3D unfoldings could however be of broader interest. | |
Mar 1, 2015 at 3:28 | comment | added | Igor Pak | You might like a movie on the 2D case: etudes.ru/ru/etudes/cubisme | |
Mar 1, 2015 at 1:05 | comment | added | Joseph O'Rourke | @TheMaskedAvenger: I don't understand the phrase "the (polycube version of the) octomino count." | |
Mar 1, 2015 at 1:03 | comment | added | The Masked Avenger | How does this compare with the (polycube version of the) octomino count? It might be easier to list those which are not unfoldings of the tesseract. | |
Mar 1, 2015 at 0:54 | comment | added | Joseph O'Rourke | An unusual question in that I am kinda hoping no one answers. | |
Feb 28, 2015 at 18:09 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |