Polyominoes

[Lewis]

Impressive! Is that using the Kadon sets?

This one was just done with sets I'd made myself - I had cut the heptominoes way back in high school, so I had to ensure that the other sets I made more recently were size compatible. I've got some polyhexes and octiamonds from Kadon though.

[Entity Valkyrie 2]

deleted

[toroidalet]

What's the smallest genus-1 n-omino whose interior can be tiled by n-ominoes? (I don't even know if they exist)

[GUYTU6J]

Wow, I don't know there's another thread other than viewtopic.php?f=12&t=3036 that is about polyominoes and tilings... How do you guys develop and verify the aperiodic tilings?
I'm trying to design aperiodic tilings myself by substitutions after reading Tilings Encyclopedia, but I don't know how to work with polyominoes. I've even attempted to submit my results, something like

Code: Select all

x = 757, y = 413, rule = B3/S23
345b412o$345b412o$345b412o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b
3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b
3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o
12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o
$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b
3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o12b3o27b3o12b4o27b3o
12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o
12b3o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b
3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o12b3o27b3o12b4o
27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o
28b3o12b3o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b
3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o12b3o27b3o
12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o
12b3o28b3o12b3o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b
3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o12b3o
27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o
27b3o12b3o28b3o12b3o$345b3o27b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b
3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$345b3o27b3o
12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o
12b3o27b3o12b3o28b3o12b3o$345b33o12b79o12b18o12b49o12b64o12b48o12b34o
12b3o$345b33o12b79o12b18o12b49o12b64o12b48o12b34o12b3o$345b33o12b79o
12b18o12b49o12b64o12b48o12b34o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b
3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o
12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b
3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o
12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b
3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o
12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b
3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o
12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b
3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o
12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b
3o12b3o27b3o13b3o12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o
12b3o27b3o12b3o12b3o12b4o12b3o12b3o$345b3o12b33o12b34o12b33o12b49o12b
18o12b33o13b48o12b18o12b34o$345b3o12b33o12b34o12b33o12b49o12b18o12b33o
13b48o12b18o12b34o$345b3o12b33o12b34o12b33o12b49o12b18o12b33o13b48o12b
18o12b34o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b
3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o
27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o
13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b
3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b
3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o
12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b
3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b
3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o
12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o
12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b
3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o
12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o
12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b
4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b
3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o
13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b
3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b
3o12b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o
12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o
12b3o12b3o12b4o27b3o$345b63o12b170o12b155o$345b63o12b170o12b155o$345b
63o12b170o12b155o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b3o
12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b
3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b
3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o
12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o
12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b
3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$
345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b
3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o
12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b
3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b
3o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b
3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b
3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o
12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o$345b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b
3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o
12b3o12b3o12b4o12b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o12b3o12b3o12b3o28b3o12b3o$345b78o12b19o12b48o12b79o12b64o12b49o
12b3o$345b78o12b19o12b48o12b79o12b64o12b49o12b3o$345b78o12b19o12b48o
12b79o12b64o12b49o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o
12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b
3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b
3o12b3o12b3o27b4o12b3o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o
12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b
3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b
3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o
27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o
$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b
3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o
12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o
12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b
3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b3o27b3o27b3o12b4o
12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o
12b3o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b
3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b3o27b3o27b3o
12b4o12b3o12b3o27b3o12b3o12b3o13b3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o
27b4o12b3o12b3o$345b3o12b3o27b3o27b3o12b4o12b3o12b3o27b3o12b3o12b3o13b
3o27b3o27b3o12b3o13b3o27b3o12b3o12b3o27b4o12b3o12b3o$345b3o12b79o12b
48o12b18o13b78o13b33o12b49o12b18o$345b3o12b79o12b48o12b18o13b78o13b33o
12b49o12b18o$345b3o12b79o12b48o12b18o13b78o13b33o12b49o12b18o$345b3o
12b3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o
27b3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b
3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b3o12b
3o12b3o27b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o27b3o
12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o12b4o
12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b
3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$345b3o
12b3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o
27b3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b
3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b3o12b
3o12b3o27b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o27b3o
12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o12b4o
12b3o12b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b
3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$124b48o
173b3o12b3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b
3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$124b48o173b3o12b
3o12b3o12b3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b
3o13b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o$124b48o173b3o12b3o12b3o12b
3o12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b
3o12b3o12b3o27b3o12b4o12b3o12b3o$124b3o27b3o12b3o173b3o12b3o12b3o12b3o
12b3o27b4o12b3o27b3o12b3o12b3o12b3o13b3o12b3o12b3o12b3o27b3o13b3o12b3o
12b3o12b3o27b3o12b4o12b3o12b3o$124b3o27b3o12b3o173b18o12b170o12b79o12b
109o$124b3o27b3o12b3o173b18o12b170o12b79o12b109o$124b3o27b3o12b3o173b
18o12b170o12b79o12b109o$124b3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b
3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b
3o12b3o28b3o12b3o$124b3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o
27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o
28b3o12b3o$124b3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o
12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o
12b3o$124b3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o
27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o
$124b3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o
12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$124b
3o27b3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o
13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$124b3o27b
3o12b3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o13b3o
12b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$124b3o27b3o12b
3o173b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o
12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$124b33o12b3o173b3o
12b3o12b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o
12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$124b33o12b3o173b3o12b3o12b3o
12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o
12b3o12b3o27b3o12b3o28b3o12b3o$124b33o12b3o173b3o12b3o12b3o12b3o12b3o
12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o
27b3o12b3o28b3o12b3o$124b3o12b3o12b3o12b3o173b3o12b3o12b3o12b3o12b3o
12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o
27b3o12b3o28b3o12b3o$124b3o12b3o12b3o12b3o173b3o12b3o12b3o12b3o12b3o
12b3o12b4o27b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o
27b3o12b3o28b3o12b3o$124b3o12b3o12b3o12b3o173b33o12b18o12b49o12b33o12b
34o12b33o12b34o12b79o12b3o$124b3o12b3o12b3o12b3o173b33o12b18o12b49o12b
33o12b34o12b33o12b34o12b79o12b3o$10b18o96b3o12b3o12b3o12b3o173b33o12b
18o12b49o12b33o12b34o12b33o12b34o12b79o12b3o$10b18o96b3o12b3o12b3o12b
3o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o12b3o$10b18o40b3o53b3o12b
3o12b3o12b3o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b3o
28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o12b3o$10b3o12b
3o40b6o50b3o12b3o12b3o12b3o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o
12b3o$10b3o12b3o41b9o46b3o12b3o12b3o12b3o173b3o27b3o12b3o12b3o12b3o28b
3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b
3o12b4o12b3o12b3o$10b3o12b3o42b11o43b3o12b3o12b3o12b3o173b3o27b3o12b3o
12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o12b3o27b3o12b4o12b3o12b3o$10b3o12b3o42b14o40b3o12b3o12b3o12b3o
173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b
3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o12b3o$10b3o12b3o43b17o36b3o
12b3o12b3o12b3o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b
3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o12b3o$10b3o
12b3o10b53o33b3o12b33o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o12b3o
$10b3o12b3o10b54o32b3o12b33o173b3o27b3o12b3o12b3o12b3o28b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o12b3o
12b3o$10b3o12b3o10b53o33b3o12b33o173b3o27b3o12b3o12b3o12b3o28b3o12b3o
12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b4o
12b3o12b3o$10b3o12b3o42b17o37b3o12b3o27b3o173b3o27b3o12b3o12b3o12b3o
28b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o
27b3o12b4o12b3o12b3o$10b3o12b3o42b13o41b3o12b3o27b3o173b3o27b3o12b3o
12b3o12b3o28b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o12b3o27b3o12b4o12b3o12b3o$10b3o12b3o41b9o46b3o12b3o27b3o173b48o
12b49o12b18o12b79o12b79o12b33o12b34o$10b3o12b3o40b7o49b3o12b3o27b3o
173b48o12b49o12b18o12b79o12b79o12b33o12b34o$10b18o41b2o53b3o12b3o27b3o
173b48o12b49o12b18o12b79o12b79o12b33o12b34o$10b18o96b3o12b3o27b3o173b
3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b
3o27b3o12b3o12b3o12b3o12b4o27b3o$10b18o96b3o12b3o27b3o173b3o12b3o27b3o
12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o
12b3o12b3o12b4o27b3o$124b3o12b3o27b3o173b3o12b3o27b3o12b3o27b4o12b3o
12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o
27b3o$124b3o12b3o27b3o173b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o
27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$124b3o12b
3o27b3o173b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o
12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$124b3o12b3o27b3o173b3o
12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o
27b3o12b3o12b3o12b3o12b4o27b3o$124b3o12b3o27b3o173b3o12b3o27b3o12b3o
27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o
12b3o12b4o27b3o$124b48o173b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o
27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$124b48o
173b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b
3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$124b48o173b3o12b3o27b3o12b3o27b
4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b
3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o
27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b
3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b
3o12b3o12b4o27b3o$345b336o12b64o$345b336o12b64o$345b336o12b64o$345b3o
12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o
28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b
3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b
3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o
12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b
3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b
3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b
3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b
3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o
27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o
28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b
3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o
12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b
3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$
345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b
3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o
12b4o27b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o
12b3o28b3o12b3o$345b18o12b48o12b34o12b18o12b49o12b79o12b33o12b49o$345b
18o12b48o12b34o12b18o12b49o12b79o12b33o12b49o$345b18o12b48o12b34o12b
18o12b49o12b79o12b33o12b49o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o
27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o12b
3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o12b3o
27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o
12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o12b
3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b
4o27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o
12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o12b
3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b
3o12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o
12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o
12b4o27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b
3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o
12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o
13b3o12b3o12b3o27b3o12b3o12b4o27b3o$345b3o12b3o12b3o27b3o12b3o12b4o12b
3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b
3o12b4o27b3o$108b94o143b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b
3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o27b3o$
108b94o143b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o12b3o12b3o12b3o28b3o
12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o12b4o27b3o$108b94o143b3o
12b48o12b19o12b33o12b49o12b18o12b33o13b78o12b34o$108b3o12b3o12b3o13b3o
27b3o12b3o143b3o12b48o12b19o12b33o12b49o12b18o12b33o13b78o12b34o$108b
3o12b3o12b3o13b3o27b3o12b3o143b3o12b48o12b19o12b33o12b49o12b18o12b33o
13b78o12b34o$108b3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o27b3o12b3o12b3o
12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o
27b3o12b4o12b3o12b3o$108b3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o27b3o
12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o
27b3o12b3o27b3o12b4o12b3o12b3o$108b3o12b3o12b3o13b3o27b3o12b3o143b3o
12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o
12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$108b3o12b3o12b3o13b3o27b3o12b
3o143b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o
12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$33o75b3o12b3o12b3o
13b3o27b3o12b3o143b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b
3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$33o75b
3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o
12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o
12b3o$33o75b3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o27b3o12b3o12b3o12b4o
12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o
12b4o12b3o12b3o$3o27b3o44b4o27b3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o
27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o
13b3o27b3o12b3o27b3o12b4o12b3o12b3o$3o27b3o44b7o24b3o12b3o12b3o13b3o
27b3o12b3o143b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b
3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$3o27b3o45b
10o20b3o12b3o12b3o13b3o27b3o12b3o143b3o12b3o27b3o12b3o12b3o12b4o12b3o
27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o
12b3o12b3o$3o27b3o46b12o17b18o12b49o12b3o143b3o12b3o27b3o12b3o12b3o12b
4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b
3o12b4o12b3o12b3o$3o27b3o46b16o13b18o12b49o12b3o143b3o12b3o27b3o12b3o
12b3o12b4o12b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o
12b3o27b3o12b4o12b3o12b3o$3o27b3o46b19o10b18o12b49o12b3o143b245o12b
125o12b18o$3o27b3o7b60o8b3o12b3o12b3o28b3o12b3o12b3o143b245o12b125o12b
18o$3o27b3o7b60o8b3o12b3o12b3o28b3o12b3o12b3o143b245o12b125o12b18o$3o
27b3o46b19o10b3o12b3o12b3o28b3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b
4o27b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b
3o12b4o12b3o12b3o$3o27b3o46b15o14b3o12b3o12b3o28b3o12b3o12b3o143b3o27b
3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b
3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$3o27b3o45b11o19b3o12b3o12b3o28b
3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o
12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$3o27b3o
44b8o23b3o12b3o12b3o28b3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b4o27b
3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b
4o12b3o12b3o$33o44b5o26b3o12b3o12b3o28b3o12b3o12b3o143b3o27b3o12b3o12b
3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b
3o27b3o12b3o12b4o12b3o12b3o$33o75b3o12b3o12b3o28b3o12b3o12b3o143b3o27b
3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b
3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$33o75b3o12b3o12b3o28b3o12b3o12b
3o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o12b3o12b3o
12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$108b3o12b3o12b3o28b
3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o
12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$108b3o12b
3o12b3o28b3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o
12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
$108b3o12b3o12b3o28b3o12b3o12b3o143b3o27b3o12b3o12b3o12b3o12b4o27b3o
12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o
12b3o12b3o$108b3o12b49o12b18o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o
27b3o12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o
12b3o$108b3o12b49o12b18o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o
12b3o28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
$108b3o12b49o12b18o143b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o
28b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$108b
3o12b3o28b3o12b3o12b3o12b3o143b63o12b49o12b79o12b33o12b19o12b48o12b34o
12b3o$108b3o12b3o28b3o12b3o12b3o12b3o143b63o12b49o12b79o12b33o12b19o
12b48o12b34o12b3o$108b3o12b3o28b3o12b3o12b3o12b3o143b3o12b3o27b3o12b3o
12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o
12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o12b3o12b3o143b3o12b3o27b3o
12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o
27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o12b3o12b3o143b3o12b3o
27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o
12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o12b3o12b3o143b3o
12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o
13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o12b3o12b3o
143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b
3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o12b3o
12b3o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b
3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o12b3o
12b3o12b3o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b
3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o28b3o
12b3o12b3o12b3o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b
3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o12b3o
28b3o12b3o12b3o12b3o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b
3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b3o
12b3o28b3o12b3o12b3o12b3o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b
3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$
108b94o143b3o12b3o27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o
12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o28b3o12b3o$108b94o143b3o12b3o
27b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o
12b3o27b3o12b3o12b3o28b3o12b3o$108b94o143b3o12b3o27b3o12b3o12b3o28b3o
12b3o12b3o12b3o27b3o13b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o
28b3o12b3o$345b3o12b33o12b49o12b18o12b33o13b78o13b48o12b64o$345b3o12b
33o12b49o12b18o12b33o13b78o13b48o12b64o$345b3o12b33o12b49o12b18o12b33o
13b78o13b48o12b64o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o
12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b
3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b
3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b3o12b3o
27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o
12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b
3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$
345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b
3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b3o
12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o
12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b
3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b
3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o
27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b
3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b
3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o
12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o
27b3o$345b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b
3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o12b3o
12b3o12b3o27b4o12b3o12b3o12b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o
27b3o12b3o12b3o12b3o12b4o27b3o$345b18o12b124o12b246o$345b18o12b124o12b
246o$345b18o12b124o12b246o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o
12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b
3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o
12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o
12b3o12b3o12b3o12b3o28b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b
3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b
3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o
12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$117b48o180b3o
12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o
12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$117b48o180b3o12b3o12b3o12b3o
27b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o$117b48o180b3o12b3o12b3o12b3o27b3o12b4o27b3o
12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o
28b3o12b3o$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o
12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o
12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o
$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o
12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$117b
3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o27b3o12b3o12b3o12b3o12b3o
13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$117b3o27b
3o12b3o180b33o12b79o12b33o12b19o12b48o12b34o12b18o12b49o12b3o$117b3o
27b3o12b3o180b33o12b79o12b33o12b19o12b48o12b34o12b18o12b49o12b3o$117b
3o27b3o12b3o180b33o12b79o12b33o12b19o12b48o12b34o12b18o12b49o12b3o$
117b3o27b3o12b3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b
3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o
27b3o12b3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b
3o27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o27b3o
12b3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b
3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o27b3o12b3o
180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b
3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o27b3o12b3o180b3o
27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o
13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b48o180b3o27b3o12b3o12b3o
27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o
12b3o12b3o27b4o12b3o12b3o$117b48o180b3o27b3o12b3o12b3o27b4o12b3o12b3o
12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o
12b3o12b3o$117b48o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o
13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b
3o12b3o27b3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o
12b3o27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o12b
3o27b3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o
27b3o12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o12b3o27b
3o180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o
12b3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o12b3o27b3o
180b3o27b3o12b3o12b3o27b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b
3o12b3o13b3o12b3o12b3o12b3o12b3o27b4o12b3o12b3o$117b3o12b3o27b3o180b
48o12b34o12b78o13b48o12b18o13b33o12b49o12b18o$117b3o12b3o27b3o180b48o
12b34o12b78o13b48o12b18o13b33o12b49o12b18o$117b3o12b3o27b3o180b48o12b
34o12b78o13b48o12b18o13b33o12b49o12b18o$117b3o12b3o27b3o180b3o12b3o27b
3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b
3o12b3o27b3o12b4o12b3o12b3o$117b3o12b3o27b3o180b3o12b3o27b3o12b3o12b3o
12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o
12b4o12b3o12b3o$117b3o12b3o27b3o180b3o12b3o27b3o12b3o12b3o12b4o12b3o
27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o
12b3o$117b3o12b3o27b3o180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o
27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b
18o95b3o12b3o27b3o180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o
13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b18o95b
3o12b33o180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o
12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b18o95b3o12b33o
180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b
3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b33o180b3o
12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o
13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b3o12b3o12b3o180b
3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b3o12b
3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b3o12b3o12b3o
180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o12b
3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b3o12b3o12b
3o180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b3o
12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b3o12b3o
12b3o180b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o27b3o13b3o27b3o12b
3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o12b3o12b3o$4b3o12b3o95b3o12b3o12b
3o12b3o180b63o12b337o$4b3o12b3o95b3o12b3o12b3o12b3o180b63o12b337o$4b3o
12b3o50b4o41b3o12b3o12b3o12b3o180b63o12b337o$4b3o12b3o50b7o38b3o12b3o
12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o12b
3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o51b10o34b3o
12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b
3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o52b12o
31b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b
3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o52b
16o27b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o
12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o
52b19o24b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b
3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b
3o13b60o22b18o12b18o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b
3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o13b
60o22b18o12b18o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b
3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o52b19o
24b18o12b18o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o28b3o
12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o52b15o28b
3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o12b3o
28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o51b
11o33b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b3o
12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b3o
50b8o37b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o27b
3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o12b
3o50b5o40b3o12b3o12b3o12b3o180b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o
27b3o12b3o28b3o12b3o27b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o$4b3o
12b3o95b3o12b3o12b3o12b3o180b33o12b33o12b79o12b79o12b19o12b48o12b49o$
4b3o12b3o95b3o12b3o12b3o12b3o180b33o12b33o12b79o12b79o12b19o12b48o12b
49o$4b3o12b3o95b3o12b3o12b3o12b3o180b33o12b33o12b79o12b79o12b19o12b48o
12b49o$4b3o12b3o95b3o12b3o12b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o12b
3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o12b
3o12b4o27b3o$4b3o12b3o95b3o12b3o12b3o12b3o180b3o12b3o12b3o12b3o27b3o
12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o
12b3o12b3o12b4o27b3o$4b3o12b3o95b3o12b3o12b3o12b3o180b3o12b3o12b3o12b
3o27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b
3o27b3o12b3o12b3o12b4o27b3o$4b3o12b3o95b3o12b3o12b3o12b3o180b3o12b3o
12b3o12b3o27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o
13b3o12b3o27b3o12b3o12b3o12b4o27b3o$4b18o95b3o12b3o12b3o12b3o180b3o12b
3o12b3o12b3o27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b
3o13b3o12b3o27b3o12b3o12b3o12b4o27b3o$4b18o95b3o12b3o12b3o12b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o
12b3o13b3o12b3o27b3o12b3o12b3o12b4o27b3o$4b18o95b33o12b3o180b3o12b3o
12b3o12b3o27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o
13b3o12b3o27b3o12b3o12b3o12b4o27b3o$117b33o12b3o180b3o12b3o12b3o12b3o
27b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o
27b3o12b3o12b3o12b4o27b3o$117b33o12b3o180b3o12b3o12b3o12b3o27b3o12b4o
12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o
12b3o12b4o27b3o$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o12b3o
27b3o12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o12b3o
12b4o27b3o$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o12b3o27b3o
12b3o12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o12b3o12b4o
27b3o$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o12b3o27b3o12b3o
12b3o12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o12b3o12b4o27b3o
$117b3o27b3o12b3o180b3o12b3o12b3o12b3o27b3o12b4o12b3o27b3o12b3o12b3o
12b3o13b3o27b3o12b3o12b3o12b3o13b3o12b3o27b3o12b3o12b3o12b4o27b3o$117b
3o27b3o12b3o180b3o12b79o12b33o12b33o13b33o12b33o13b48o12b18o12b34o$
117b3o27b3o12b3o180b3o12b79o12b33o12b33o13b33o12b33o13b48o12b18o12b34o
$117b3o27b3o12b3o180b3o12b79o12b33o12b33o13b33o12b33o13b48o12b18o12b
34o$117b3o27b3o12b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b
3o13b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$
117b3o27b3o12b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b
3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o
27b3o12b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b
3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o27b3o
12b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b3o12b
3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o27b3o12b3o
180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b
3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b48o180b3o12b3o27b
3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o13b3o27b
3o12b3o12b3o12b3o12b4o12b3o12b3o$117b48o180b3o12b3o27b3o12b3o27b4o12b
3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b
3o12b4o12b3o12b3o$117b48o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b
3o27b3o13b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b
3o$117b3o12b3o27b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o
13b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b
3o12b3o27b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o
12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o12b
3o27b3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b3o
12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b
3o180b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o12b3o12b3o
12b3o27b3o13b3o27b3o12b3o12b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b3o
180b109o12b79o12b170o12b18o$117b3o12b3o27b3o180b109o12b79o12b170o12b
18o$117b3o12b3o27b3o180b109o12b79o12b170o12b18o$117b3o12b3o27b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b3o12b3o27b3o180b3o
12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o
12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b48o180b3o12b3o12b3o
12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o12b3o12b3o
28b3o12b3o27b3o12b3o12b4o12b3o12b3o$117b48o180b3o12b3o12b3o12b3o27b3o
12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o
27b3o12b3o12b4o12b3o12b3o$117b48o180b3o12b3o12b3o12b3o27b3o12b4o12b3o
12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o
12b4o12b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b
3o13b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$
345b3o12b3o12b3o12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b
3o12b3o12b3o12b3o28b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o27b3o12b4o12b3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o12b3o12b3o
28b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o27b3o12b4o12b
3o12b3o12b3o27b3o12b3o13b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o27b3o12b
3o12b4o12b3o12b3o$345b18o12b48o12b34o12b79o12b18o12b49o12b79o12b3o$
345b18o12b48o12b34o12b79o12b18o12b49o12b79o12b3o$345b18o12b48o12b34o
12b79o12b18o12b49o12b79o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b
3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$
345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b
3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o
27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o
12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b
3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o12b3o12b3o27b3o12b3o
12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o
28b3o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b
3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o12b3o12b3o27b3o
12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o
27b3o28b3o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b
3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o12b3o12b3o
27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o
12b3o27b3o28b3o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b
3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o12b3o
12b3o27b3o12b3o12b4o27b3o12b3o12b3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o
12b3o12b3o27b3o28b3o12b3o$345b3o12b3o12b3o27b3o12b3o12b4o27b3o12b3o12b
3o27b3o28b3o12b3o12b3o12b3o28b3o12b3o12b3o12b3o27b3o28b3o12b3o$345b3o
12b48o12b64o12b79o12b49o12b18o12b79o$345b3o12b48o12b64o12b79o12b49o12b
18o12b79o$345b3o12b48o12b64o12b79o12b49o12b18o12b79o$345b3o12b3o27b3o
12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b3o
12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b
3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o12b
4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o
27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b
3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b
3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o
27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o
12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b
3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o
27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o
12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b
3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b
3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o
13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b
3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b
3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o
12b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o
12b3o12b4o27b3o$345b3o12b3o27b3o12b3o12b3o12b4o12b3o27b3o12b3o12b3o12b
3o13b3o27b3o12b3o27b3o13b3o12b3o12b3o12b3o12b3o12b3o12b4o27b3o$345b
154o12b170o12b64o$345b154o12b170o12b64o$345b154o12b170o12b64o$345b3o
27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o
12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b
4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b
3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b3o
12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b
3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b
3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o
12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o
12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b
3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$
345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b
3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o
12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o
12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b
3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b
3o$345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o
12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b
3o12b3o12b4o27b3o12b3o12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b
3o12b3o12b3o12b3o28b3o12b3o$345b3o27b3o12b3o12b3o12b3o12b4o27b3o12b3o
12b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o28b3o12b3o12b3o12b3o12b3o28b3o
12b3o$345b33o12b18o12b49o12b33o12b19o12b48o12b34o12b33o12b34o12b3o$
345b33o12b18o12b49o12b33o12b19o12b48o12b34o12b33o12b34o12b3o$345b33o
12b18o12b49o12b33o12b19o12b48o12b34o12b33o12b34o12b3o$345b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o
12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b
3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o
12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b
3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o
12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b
3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o
12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b
3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o
12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b
3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b
3o12b4o12b3o12b3o$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o
12b3o13b3o12b3o27b3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o
$345b3o12b3o12b3o12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b
3o12b3o12b3o13b3o12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b3o12b3o
12b3o12b3o12b3o28b3o12b3o12b3o27b3o12b3o13b3o12b3o27b3o12b3o12b3o13b3o
12b3o12b3o27b3o12b3o12b4o12b3o12b3o$345b3o12b33o12b49o12b63o13b48o12b
18o13b78o12b34o$345b3o12b33o12b49o12b63o13b48o12b18o13b78o12b34o$345b
3o12b33o12b49o12b63o13b48o12b18o13b78o12b34o$345b3o12b3o27b3o12b3o27b
4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b
3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o
27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o$345b3o12b3o27b3o12b
3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b
3o27b3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o
13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o$345b3o12b3o27b
3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b
3o12b3o27b3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o
27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o$345b3o12b
3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b
3o27b3o12b3o27b3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o
12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o$345b
3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b
3o13b3o27b3o12b3o27b3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o12b3o
12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o
$345b3o12b3o27b3o12b3o27b4o12b3o12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b
3o12b3o13b3o27b3o12b3o27b3o12b4o27b3o$345b3o12b3o27b3o12b3o27b4o12b3o
12b3o12b3o12b3o27b3o13b3o27b3o12b3o12b3o12b3o13b3o27b3o12b3o27b3o12b4o
27b3o$345b412o$345b412o$345b412o!
#C [[ VIEWONLY ]]

Is there a summary about self-tiling polyominoes? I wonder if the R-pentomino can be tiled by smaller copies of itself.

[toroidalet]

This 23-omino can fit another completely inside it:

Code: Select all

x = 7, y = 7, rule = B/S012345678
b5o$2o4bo$o5bo$o5bo$o5bo$o4b2o$6o!

If the diagonal connection disqualifies it, the answer is 24 (the most obvious example is the perimeter of a 6*8 rectangle). No smaller polyomino can enclose an area ≥ its own

How do you guys develop and verify the aperiodic tilings?

All the tilings on this thread (except the one from MathWorld) are reductions from known aperiodic sets, so we only have to prove that tilings that don't follow the grid don't work/are still aperiodic.

I wonder if the R-pentomino can be tiled by smaller copies of itself.

It can't. There is only one way to occupy the corner of one of the big squares, and then the red cell cannot be occupied:

Code: Select all

x = 10, y = 10, rule = LifeHistory
6.2B2A$B.B.B.B2AD$6.2BAB$6.4B2$8.B2$8.B2$8.B!

This is my 1111th post.

[ColorfulGalaxy]

Anyone else on here have an interest in polyominoes or other polyforms (outside of a cellular-automata context, I suppose)?
I've been playing on with various sets a fair bit recently, pentominoes and hexominoes mainly, just constructing (or attempting to construct) rectangles and other shapes with them. The most interesting/challenging thing I've managed to make so far is the construction in the picture below, all 108 heptominoes into a 29x29 square with a symmetrical hole.

[a thing]

I find this really fascinating. I might try to see if something similar is possible with different size polyominoes.
(By hand)

I made a wiki article about polyominoes.
I'm planning on listing all polyominoes with less than 9 cells.

[HelicopterCat3]

Anyone else on here have an interest in polyominoes or other polyforms (outside of a cellular-automata context, I suppose)?
I've been playing on with various sets a fair bit recently, pentominoes and hexominoes mainly, just constructing (or attempting to construct) rectangles and other shapes with them. The most interesting/challenging thing I've managed to make so far is the construction in the picture below, all 108 heptominoes into a 29x29 square with a symmetrical hole.

[a thing]

I find this really fascinating. I might try to see if something similar is possible with different size polyominoes.
(By hand)

I made a wiki article about polyominoes.
I'm planning on listing all polyominoes with less than 9 cells.

Wait, why do we need another article on polyominoes when we already have one? I'm just curious

[ColorfulGalaxy]

I find this really fascinating. I might try to see if something similar is possible with different size polyominoes.
(By hand)

I made a wiki article about polyominoes.
I'm planning on listing all polyominoes with less than 9 cells.

Wait, why do we need another article on polyominoes when we already have one? I'm just curious

I'm planning on adding some more features about polyominoes, such as evolution in OCA, perimeter/area of minimum covering convex polygon.

[HelicopterCat3]

I made a wiki article about polyominoes.
I'm planning on listing all polyominoes with less than 9 cells.

Wait, why do we need another article on polyominoes when we already have one? I'm just curious

I'm planning on adding some more features about polyominoes, such as evolution in OCA, perimeter/area of minimum covering convex polygon.

Oh sweet! That can be handy

[ColorfulGalaxy]

My two cents: anyone interested in polyomino problems might want to page through the archives on www.mathpuzzle.com. There's something omino-related in almost every annual / bi-monthly / monthly archive, like this from 29 March 2005:

rep12y.gif
That was apparently an unusually tricky problem to solve... See also the tiling problems at the end of 2012, and the huge multi-omino bulls-eye in 2011, and the links from those entries to other polyomino websites, and the "Polyominoes" page in the right sidebar which is also full of interesting links.

Hello, I just finished the "Pentominoes" section of my list and thanks for your support.
Now I'm working on the hexominoes section.
I'm also planning to add heptominoes and octominoes.
http://conwaylife.com/wiki/User:Colorfu ... by_apgcode

[ColorfulGabrielsp138]

What is the smallest polyomino that can perform 3-color tiling but not 2-color tiling?
("Color" as in "four color theorem")
I assume that it's the U-pentomino, but I'm not sure whether it can also do 2-color tiling.

EDIT: Partial proof:

The U-pentomino shows a "pit" with 3 cells in its von Neumann neighborhood, as shown below:

Code: Select all

x = 0, y = 0, rule = LifeHistory
2o$oD$2o!

This "pit" has to be filled by another U-pentomino like this:

Code: Select all

x = 0, y = 0, rule = LifeHistory
2o$o2C$2oC$b2C!

or

Code: Select all

x = 0, y = 0, rule = LifeHistory
b2C$2oC$o2C$2o!

In both cases, this will leave a cell that must take a third color:

Code: Select all

x = 0, y = 0, rule = LifeHistory
2o$o2C$2oC$D2C!

Code: Select all

x = 0, y = 0, rule = LifeHistory
D2C$2oC$o2C$2o!

The rest of the proof can be seen on my LifeWiki article.

[confocaloid]

The 35 hexominoes cover 210 cells; if you add three gliders you get 225 = 15x15. So I wanted to try to synthesize a p15 oscillator in a 15x15 square filled with hexominoes and gliders:

sols.png (3 KiB) Viewed 4756 times

[Lewis]

A 79x147 rectangle with a complete set of nonominoes:



The solution was found by hand, here's a photo of the physical pieces:


Total solve time was approximately 12-14 hours, spread out over a couple of weeks. I think nonominoes are as high as I'm going to go; I don't think I could fit a set of dekominoes anywhere, let alone have the patience to tile anything with them.

[googleplex]

Aperiodic Polyomino tiling, based off of the trilobite and crab tiling, Pop 76:

Code: Select all

x = 19, y = 8, rule = //5
2B2.B.2B7.A$3B.4B5.A.2A$.6B5.6A$2.4B7.6A$8B3.6A$.6B5.6A$2.B.4B5.2A.A$
4.B.2B6.A!

Code: Select all

x = 32, y = 30, rule = //5
2$8.A5.C4.B2.2B.A$6.A.2A2.C.2C2.2B.3B2A.A$5.6A6C6B6A$6.6A6C4B6A$4.6A6C
8B6A$5.6A6C6B6A$4.2D2ADA2D2CAC4BC3BAD2A2D$4.3DA4DAC2A2BCB2C2B2DA3D$5.
6D6A6C6D$4.8D6A6C4D$6.4D6A6C8D$5.6D6A6C6D$4.3DC2D2B2ABA2B2CAC4DC3D$4.
2D2CDC3BA4BAC2A2DCD2C2D$5.6C6B6A6C$4.6C8B6A6C$6.6C4B6A6C$5.6C6B6A6C$6.
CA2C3BC2B2D2ADA2D2CAC$6.2ACA2B2CBC3DA4DAC2A$5.6A6C6D6A$4.6A6C8D6A$6.6A
6C4D6A$5.6A6C6D6A$6.A.2A2.C.2C3D.2D2.2A.A$8.A5.C.2D2.D4.A!

[Citation needed]

Code: Select all

x = 20, y = 3, rule = ColourisedLife27s
2UX3PpB4pAWTR3S3V$U3X2P3pBpA2WT3R2SQV$2UX5OpB2W3TR4QV!

Code: Select all

x = 11, y = 11, rule = ColourisedLife27s
4.3V$4.2QV$4.QWV$4.Q2W$4pAQpB2W2RP$UpAU3pBX2R2P$3UpBO3XR2P$4.OSX$4.O2S
$4.OTS$4.OTS$4.3T!

Code: Select all

x = 8, y = 8, rule = ColourisedLife27s
bPQ3VX$2PQVW3X$2PQV2WXO$T2Q2pB2WO$3TpB2UpAO$TR2pBU2pAO$2R2S2UpAO$b2R3SpA!

Code: Select all

x = 11, y = 6, rule = ColourisedLife27s
T5OQpA3V$3T4Q2pARV$TX2pB3bpA2RV$3XpB3bpAW2R$UXU2pB2S2W2P$3U3S2W3P!

Code: Select all

x = 21, y = 3, rule = ColourisedLife27s
2UX4pAR3T2pB2W3S3V$U3XbpA3RTbpB2P2Wb2SQV$2UX5ORT2pB3PW4QV!

Code: Select all

x = 11, y = 11, rule = ColourisedLife27s
4.3T$4.OTS$4.OTS$3.WO2SR$2U2WOS3RpBV$U2WpAObR3pBV$2U4pAXpB3V$3.2Q3X$4.
QPX$4.Q2P$4.Q2P!

Code: Select all

x = 30, y = 3, rule = ColourisedLife27s
2UX3P2pBW4pA3SRT4L2F2BH3V$U3X2PQpB2WpAD2S3RT2NL2F3B3HV$2UX4Q2pB2W4DR3T3NF5OHV!

[confocaloid]

Crossposting a two-state R3 INT CA that solves the problem "every pentomino must be a still-life, but there must be some spaceships":

In this two-state isotropic cellular automaton on the square tiling with range-3 weighted neighbourhood,

• the twelve pentominoes are still-life objects,
• the glider is also a still-life object, however, the fishes are kept,
• four p2 oscillators from Conway's Life (blinker, beacon, clock, toad) are preserved,
• there is an alien p12 mod3 oscillator.

Code: Select all

x = 64, y = 56, rule = R3,C0,S15-52,132-159,248-275,379-391,496-510,613-627,743,978,B39,42,158,274-275,391-395,507-511,624-629,743-746,859-863,981,1214,NW007575017575007501750175017575750D0D0D757501010D000D010175750D0D0D75757501750175017500757501757500
31bobo$31bobo$33bo$31bo11$21bo$21bo9bo20bo$11b2o8bo9bo9b2o9bo$10b2o9bo
9bo9b2o8b2o$11bo9bo9b2o8bo9bo8$3o18bo9bo10bo9bo8b2o$bo8bobo8bo9b2o8b3o
7b2o9bo$bo8b3o8b3o8b2o8bo9bo9b2o$52bo10$3bo9b2o13bo11b3o12bo$3bo9b2o
11b2o11b3o14bo$3bo11b2o11b2o24b3o$15b2o10bo9$9b2o19bo$7bo4bo15bo3bo16b
o2bo$13bo19bo19bo$7bo5bo14bo4bo15bo3bo$8b6o15b5o16b4o!
#C [[ THEME MCell GRID ]]

The weighted neighbourhood is the following (weights in hexadecimal, '0D' means 13, '75' means 117):

Code: Select all

00 75 75 01 75 75 00
75 01 75 01 75 01 75
75 75 0D 0D 0D 75 75
01 01 0D 00 0D 01 01
75 75 0D 0D 0D 75 75
75 01 75 01 75 01 75
00 75 75 01 75 75 00

[d/dx]

All five fourominoes arranged into something one away from a rectangle. Tiles the plane periodically.

Code: Select all

x = 4, y = 6, rule = JvN29
2AJ$2A2J$3FJ$NF2pC$3NpC$3.pC!

[confocaloid]

All five fourominoes arranged into something one away from a rectangle. Tiles the plane periodically.

Code: Select all

x = 4, y = 6, rule = JvN29
2AJ$2A2J$3FJ$NF2pC$3NpC$3.pC!

The tetrominoes can be arranged on a torus:

Code: Select all

x = 5, y = 4, rule = Test:T5,6
B4A$2B3E$CB2DE$2C2DC!

@RULE Test

@COLORS
0 16 16 16
1 240 16 16
2 16 240 16
3 16 16 240
4 240 240 16
5 240 240 240

@TABLE
n_states:6
neighborhood:vonNeumann
symmetries:none

var x={0,1,2,3,4,5}
var x1=x
var x2=x
var x3=x
var x4=x

x, x1,x2,x3,x4, x2

[tommyaweosme]

Here’s a rectangle which contains at least one of every hexomino

Code: Select all

x = 24, y = 18, rule = Codd
2B5C3B3AD2C2A2C2D2C$4B2AC3B3AD2C2A2C2DCB$A4D4AC3E2DC2A2CD2CB$2A2C2D2B
2C2BEDACD3BDACB$3AC3B2C2B2ED2A2DBD3AB$3B3CBC2B3DB2A2DBDACAB$3B6A3CD2B
ADCBD3CB$3C3B4DCBDCB4CDC2AE$2CA2B2A2D2CBDCB2AC2DC2AE$C3AB2A4EBACB3AB
2ACAE$2A3C2A2EA2BAC2DA2BA2CAE$3C2A3B3ABACD3B2ABC2E$B3ACBA2B2ADACD4CAB
CDA$BAB3C3A2CDA2D2CD3BCDA$3BCBCABA2CDA2C4DCBADA$4A4B2C2DBC2AD4CADA$A
4C5AD2B2C2A3BCADA$A2C6BA3BC2A3B3ADA!

Someone can 4-color mapping theorem it if they like.

here u are

Code: Select all

x = 24, y = 18, rule = Codd
2B5C3B3AB2A2C2A2D2C$4B2AC3B3AB2A2C2A2DCB$A4D4AC3D2BA2C2AD2CB$2A2C2D2B
2C2BDBCAD3BDACB$3AC3B2C2B2DB2C2DBD3AB$3D3CBC2B3AD2C2DBDACAB$3D6A3DA2D
CDABD3CB$3B3C4BDBACD4ADC2AD$2BA2C2A2B2DBACD2CA2DC2AD$B3AC2A4CBDCD3CB2A
CAD$2A3B2A2CD2BDC2AC2BA2CAD$3B2A3B3DBDCA3B2ABC2D$D3ACBA2B2DADCA4CABCB
A$DAD3C3A2CAD2A2CD3BCBA$3DCBCABA2CAD2C4DCBABA$4A4B2C2ABC2AD4CABA$A4C5D
A2B2C2A3BCABA$A2C6BD3BC2A3B3ABA!

The tetrominoes can be arranged on a torus:

Code: Select all

x = 5, y = 4, rule = Test:T5,6
B4A$2B3E$CB2DE$2C2DC!

@RULE Test

@COLORS
0 16 16 16
1 240 16 16
2 16 240 16
3 16 16 240
4 240 240 16
5 240 240 240

@TABLE
n_states:6
neighborhood:vonNeumann
symmetries:none

var x={0,1,2,3,4,5}
var x1=x
var x2=x
var x3=x
var x4=x

x, x1,x2,x3,x4, x2

Code: Select all

x = 5, y = 4, rule = Test:T5,6
B4A$2B3D$CB2AD$2C2AC!
@RULE Test

@COLORS
0 16 16 16
1 240 16 16
2 16 240 16
3 16 16 240
4 240 240 16
5 240 240 240

@TABLE
n_states:6
neighborhood:vonNeumann
symmetries:none

var x={0,1,2,3,4,5}
var x1=x
var x2=x
var x3=x
var x4=x

x, x1,x2,x3,x4, x2

Code: Select all

x = 20, y = 3, rule = ColourisedLife27s
2UX3PpB4pAWTR3S3V$U3X2P3pBpA2WT3R2SQV$2UX5OpB2W3TR4QV!

Code: Select all

x = 11, y = 11, rule = ColourisedLife27s
4.3V$4.2QV$4.QWV$4.Q2W$4pAQpB2W2RP$UpAU3pBX2R2P$3UpBO3XR2P$4.OSX$4.O2S
$4.OTS$4.OTS$4.3T!

Code: Select all

x = 8, y = 8, rule = ColourisedLife27s
bPQ3VX$2PQVW3X$2PQV2WXO$T2Q2pB2WO$3TpB2UpAO$TR2pBU2pAO$2R2S2UpAO$b2R3SpA!

Code: Select all

x = 11, y = 6, rule = ColourisedLife27s
T5OQpA3V$3T4Q2pARV$TX2pB3bpA2RV$3XpB3bpAW2R$UXU2pB2S2W2P$3U3S2W3P!

Code: Select all

x = 21, y = 3, rule = ColourisedLife27s
2UX4pAR3T2pB2W3S3V$U3XbpA3RTbpB2P2Wb2SQV$2UX5ORT2pB3PW4QV!

Code: Select all

x = 11, y = 11, rule = ColourisedLife27s
4.3T$4.OTS$4.OTS$3.WO2SR$2U2WOS3RpBV$U2WpAObR3pBV$2U4pAXpB3V$3.2Q3X$4.
QPX$4.Q2P$4.Q2P!

Code: Select all

x = 30, y = 3, rule = ColourisedLife27s
2UX3P2pBW4pA3SRT4L2F2BH3V$U3X2PQpB2WpAD2S3RT2NL2F3B3HV$2UX4Q2pB2W4DR3T3NF5OHV!

Code: Select all

x = 39, y = 31, rule = ColourisedLife27s
27.3A$27.2BA$10.AB3DA11.BCA$9.2ABDC3A10.B2C$9.2ABD2CAB6.4ABD2C2BA$9.C
2B2A2CB6.BAB3DA2B2A$9.3CA2BAB6.3BDB3AB2A$9.CB2AB2AB10.BCA$9.2B2C2BAB10.
B2C$10.2B3CA11.BAC$27.BAC$27.3A2$6.A5BCB3A$6.3A4C2BCA$6.AB2D3AB2CA$6.
3BD3ABA2C$6.CBC2D2B2A2C2.2AB3CA4BCAB3A3B$6.3C3B2A3C2.A3B2C3AB2CA3B2AC
B$19.2AB5DA2C3AB4CB4$5.2AB4CA3B2A2C3A3C$5.A3B.C3AB.A2B2C.2ABC$5.2AB5D
AB2A3BC4BC3$2AB3C2AB4A3BAB4C2B2CB3A$A3B2CDA2BAC2B3AB2AC2B3C3BA$2AB4D2A
2B4CA3B3AB5ABA!

[confocaloid]

Here’s a rectangle which contains at least one of every hexomino

Code: Select all

x = 24, y = 18, rule = Codd

Someone can 4-color mapping theorem it if they like.

here u are

Code: Select all

x = 24, y = 18, rule = Codd

Here is a smaller rectangle (18-by-12), I believe only one hexomino is duplicated here as a "hole" (and all 35 free hexominoes are present).
There are at least two points such that four tiles meet at a single point, there may be a solution avoiding any such points of contact of four tiles.

hexominoes-with-one-duplicate.png (1.74 KiB) Viewed 1889 times

[Citation needed]

ColorfulGalaxy managed to fit all of the "five-or-fewer-cell" mirror-symmetric polyominoes into a "17 by 3" rectangle.

Code: Select all

x = 17, y = 3, rule = ColourisedLife47s
2AG3RX2VND4PIC$A3GR2X2VN2D3LIQ$2AG5B3N2D3IQ!
[[ ICONS ]]

Code: Select all

#C with 3 or 4 or fewer cells
x = 7, y = 23, rule = ColourisedLife47s
pN$2Q$3G$2pJ$pJ3$pN2pJ$2QpJ$3G4$pN$2Q$3G$4A$2pD2pJN$2pDpJ3N2$4A3G$2pD
2pJN2Q$2pDpJ3NpN!