Question

How good can a "near-miss" polyomino packing be?

score 363 · Answer 1 · 2020-12-22 21:32:00

363

Views

How good can a "near-miss" polyomino packing be?

Published on 22 Dec 2020 - 21:32

score 82 · Answer 2 · 2020-12-30 00:24:04

82

Views

What is the asymptotic behavior of large polyominoes? How many of them tile the plane?

Published on 30 Dec 2020 - 0:24

score 592 · Answer 3 · 2021-01-14 18:19:57

592

Views

How quickly can you mess up a domino tiling in 3D?

Published on 14 Jan 2021 - 18:19

score 701 · Answer 4 · 2021-01-15 16:41:06

701

Views

What is the smallest polyomino that can't surround a $1\times 1$ hole?

Published on 15 Jan 2021 - 16:41

score 177 · Answer 5 · 2021-01-16 22:41:45

177

Views

If a polyomino tiles the plane, is there necessarily a larger tiling polyomino formed by two copies of it?

Published on 16 Jan 2021 - 22:41

score 166 · Answer 6 · 2021-01-18 00:04:28

166

Views

Random domino tilings: Is this distribution well-defined, and how can it be sampled from?

Published on 18 Jan 2021 - 0:04

score 113 · Answer 7 · 2021-01-28 16:33:23

113

Views

If an animal tiles the plane via translation, can it do so in a lattice configuration?

Published on 28 Jan 2021 - 16:33

score 2.2k · Answer 8 · 2021-02-09 15:20:33

2.2k

Views

If a subset of the square grid can be tiled by $1\times n$ rectangles for every $n$, can it be tiled by infinite rays?

Published on 09 Feb 2021 - 15:20

score 115 · Answer 9 · 2021-03-06 17:05:32

115

Views

Can you tile a heart with dominoes?

Published on 06 Mar 2021 - 17:05

score 260 · Answer 10 · 2021-04-28 23:06:37

260

Views

Are the only polyominoes that can tile triangles right trominoes?

Published on 28 Apr 2021 - 23:06

score 245 · Answer 11 · 2021-05-05 20:13:35

245

Views

Octahedron to tetrahedron ratio in generalized polyominoes in the tetrahedral-octahedral honeycomb

Published on 05 May 2021 - 20:13

score 405 · Answer 12 · 2021-05-17 16:37:42

405

Views

How densely can the :...: polyomino fill the plane?

Published on 17 May 2021 - 16:37

score 324 · Answer 13 · 2021-05-17 23:46:40

324

Views

Smallest non-space-filling polycube?

Published on 17 May 2021 - 23:46

score 172 · Answer 14 · 2021-05-30 19:41:52

172

Views

How many fixed polyominoes does it take to force an aperiodic tiling of the plane?

Published on 30 May 2021 - 19:41

score 245 · Answer 15 · 2021-06-02 20:29:50

245

Views

Can every polyomino of even size be tiled by $L$-trominoes when scaled up by a factor of $3$?

Published on 02 Jun 2021 - 20:29

List Question

How good can a "near-miss" polyomino packing be?

What is the asymptotic behavior of large polyominoes? How many of them tile the plane?

How quickly can you mess up a domino tiling in 3D?

What is the smallest polyomino that can't surround a $1\times 1$ hole?

If a polyomino tiles the plane, is there necessarily a larger tiling polyomino formed by two copies of it?

Random domino tilings: Is this distribution well-defined, and how can it be sampled from?

If an animal tiles the plane via translation, can it do so in a lattice configuration?

If a subset of the square grid can be tiled by $1\times n$ rectangles for every $n$, can it be tiled by infinite rays?

Can you tile a heart with dominoes?

Are the only polyominoes that can tile triangles right trominoes?

Octahedron to tetrahedron ratio in generalized polyominoes in the tetrahedral-octahedral honeycomb

How densely can the :...: polyomino fill the plane?

Smallest non-space-filling polycube?

How many fixed polyominoes does it take to force an aperiodic tiling of the plane?

Can every polyomino of even size be tiled by $L$-trominoes when scaled up by a factor of $3$?

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