POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


O tetromino and I pentomino

Prime rectangles: ≥ 79.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (6x6):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h12345678910
100
20000
3000000
400000000
50000000000
6000000000022P
70022P00440012122828P
8000000000066P36362626P
90033P0099003333108108137137838838
10000022P33P77P21211401403483481185118548764876
110044P0016161414P104104490490846846585658561538715387
120033P0017172121P1651659509502083208313094130944945949459
130055P0025252828P26326319481948376937693752237522139640139640
1400660051513535P625625415441541042310423109950109950424612424612
150066P1212P545417417491891889628962331443314428742428742417409471740947
1600101000124124327327P??????????
17001111P00139139494494P??????????
1800151500260260675675P??????????
1900181800364364870870P??????????
20002121464655955927272727??????????

Smallest prime reptiles

Smallest prime reptiles (4Ox3, 5Ix3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
O tetromino???P?P?P
I pentomino???P?P?P

See Also

O tetromino and T tetrominoO tetromino and L pentomino