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 D hexomino

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (4x8):

Smallest square (8x8):

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
800000044P44P001616P4848C
9000000000044P00156156C00
1000000099P000000≥1000≥1000C≥1000≥1000P≥1000≥1000P
1100000022P000000≥1000≥1000C00≥1000≥1000P00
120000002424P88P004040P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
130000001616P001616P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
140000008989P001616P00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
150000006868P000000≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
16000000294294C7272C00608608C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
17000000248248P004848P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
18000000951951C009696C00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
19000000934934C006464P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
20000000≥1000≥1000C298298C00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
21000000≥1000≥1000C00128128P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
22000000≥1000≥1000C00384384C≥1000≥1000P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
23000000≥1000≥1000C00512512C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
24000000≥1000≥1000C≥1000≥1000C256256P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
25000000≥1000≥1000C00320320P00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00≥1000≥1000C00
26000000≥1000≥1000C00≥1000≥1000C≥1000≥1000P????????????????
27000000≥1000≥1000C00≥1000≥1000C00????????????????
28000000≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C????????????????
29000000≥1000≥1000C00≥1000≥1000P00????????????????
30000000≥1000≥1000C00≥1000≥1000C≥1000≥1000C????????????????
31000000≥1000≥1000C00≥1000≥1000C00????????????????
32000000≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C????????????????
33000000≥1000≥1000C00≥1000≥1000C00????????????????
34000000≥1000≥1000C00≥1000≥1000C≥1000≥1000C????????????????
35000000≥1000≥1000C00≥1000≥1000C00????????????????

See Also

Z tetromino and C hexominoZ tetromino and F hexomino