Timeline for Name this periodic tiling
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2013 at 15:51 | comment | added | Nick Matteo | If you take vertices at the centres of the d-cubes and edges through the faces of the d-cubes, you just get the cubical tiling back again; it's self-dual. | |
| Oct 13, 2011 at 1:06 | comment | added | Anthony Quas | Is it obvious that for any BOX$\setminus$box, it arises as a "linear overlap tiling of a cubic tiling"? | |
| Oct 13, 2011 at 0:25 | comment | added | Anthony Quas | My condition was that multiples of $e_d$, the $d$th coordinate vector, are dense in $\mathbb R^d/M\mathbb Z^d$. Having irrational entries is the right kind of condition to get this, but is not sufficient: basically you have to ensure that $e_d$ doesn't belong to any proper closed subgroup of $\mathbb R^d/M\mathbb Z^d$. | |
| Oct 13, 2011 at 0:03 | comment | added | Ryan Budney | I'm not following your comment. In my edited response, would this condition be satisfied if the matrix $M$ had irrational entries? | |
| Oct 12, 2011 at 23:51 | history | edited | Ryan Budney | CC BY-SA 3.0 |
added 998 characters in body
|
| Oct 12, 2011 at 22:58 | comment | added | Anthony Quas | Wouldn't this give you something where translates in the original lattice directions didn't have a dense orbit? This, in fact, was the main reason for me to look at this: say the big boxes are unit cubes. If you take a point and repeatedly move by 1 in the `vertical' direction, then the images become dense in the prototile (for some choices of the sub-box). | |
| Oct 12, 2011 at 22:11 | history | edited | Ryan Budney | CC BY-SA 3.0 |
added 99 characters in body
|
| Oct 12, 2011 at 21:55 | history | answered | Ryan Budney | CC BY-SA 3.0 |