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.


Z tetromino and Y2 hexomino

Prime rectangles: ≥ 65.

Smallest rectangle tilings

Smallest known rectangle (8x10):

Smallest square (10x10):

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 \ h123456789101112131415
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
100000000000000022P001616P
1100000000000000000044P00
120000000000000044P66P66P3030P476476P
130000000000000000004848P00640640P00
140000000000002020P88P002626P144144P≥1000≥1000P≥1000≥1000P≥1000≥1000C
150000000000000044P007676P00≥1000≥1000P00≥1000≥1000C00
1600000000000088P2424P7272P304304C≥1000≥1000P≥1000≥1000C≥1000≥1000P≥1000≥1000C≥1000≥1000C
17000000000000008282P00764764P00≥1000≥1000C00≥1000≥1000C00
180000000000001616P130130P168168P≥1000≥1000C≥1000≥1000P≥1000≥1000C≥1000≥1000P≥1000≥1000C≥1000≥1000C
1900000000000000162162P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
200000000000006868P360360C≥1000≥1000P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
2100000000000000≥100≥100P00????????????
22000000000000≥100≥100P≥100≥100C≥100≥100P????????????
2300000000000000≥100≥100P00????????????
24000000000022P≥100≥100P≥100≥100C≥100≥100C????????????
2500000000000000≥100≥100C00????????????
26000000000000≥100≥100P≥100≥100C≥100≥100P????????????
27000000000044P00≥100≥100C00????????????
28000000000000≥100≥100C≥100≥100C≥100≥100C????????????
29000000000088P00≥100≥100C00????????????
3000000000001818P≥100≥100C≥100≥100C≥100≥100C????????????
31000000000000??????????????????
3200000000002222P??????????????????
3300000000003232P??????????????????
3400000000004040P??????????????????
350000000000≥100≥100P??????????????????
3600000000009292P??????????????????
370000000000≥100≥100P??????????????????
380000000000≥100≥100P??????????????????
390000000000≥100≥100P??????????????????
400000000000≥100≥100P??????????????????
410000000000≥100≥100P??????????????????
420000000000≥100≥100P??????????????????
430000000000≥100≥100P??????????????????
440000000000≥100≥100P??????????????????
450000000000≥100≥100P??????????????????
460000000000≥100≥100P??????????????????
470000000000≥100≥100P??????????????????
480000000000≥100≥100C??????????????????
490000000000≥100≥100P??????????????????
500000000000≥100≥100P??????????????????
510000000000≥100≥100C??????????????????
520000000000≥100≥100P??????????????????
530000000000≥100≥100C??????????????????
540000000000≥100≥100C??????????????????
550000000000≥100≥100P??????????????????
560000000000≥100≥100C??????????????????
570000000000≥100≥100C??????????????????
580000000000≥100≥100C??????????????????
590000000000≥100≥100C??????????????????
600000000000≥100≥100C??????????????????

See Also

Z tetromino and Y1 hexominoI pentomino and L pentomino