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 V pentomino

Prime rectangles: ≥ 43.

Smallest rectangle tilings

Smallest known rectangle (8x16):

Smallest square (12x12):

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 \ h12345678910111213141516
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
1000000000000000000000
110000000000000000000000
1200000000000000000000884040
13000000000000000000000014014000
1400000000000000000010100030030000≥100≥100
15000000000000000000000016341634????≥100≥100
160000000000000016160024240046564656??????≥256≥256
170000000000000000000000≥12000≥12000????????
18000000000000007272141414014075227522≥100≥100≥100≥100??????
1900000000000000000000??≥100≥100????????
2000000000000000404000476476??≥100≥100????????
210000000000000000404000??≥100≥100????????
220000000000000082820023502350??≥100≥100????????
2300000000000000000000????????????
24000000000000003443442862861312813128≥100≥100??≥100≥100??????
2500000000000000000000????????????
26000000000000001592159200≥1≥1????????????
27000000000000000016241624??????????????
280000000000000091691600≥100≥100????????????
29000000000000000000??????????????
3000000000000000265226521060210602??????????????
31??????????????00????????????????
32??????????????78287828????????????????
33????????????????≥100≥100??????????????
34????????????????????????????????
35????????????????????????????????
36????????????????≥100≥100??????????????

See Also

Z tetromino and U pentominoZ tetromino and Y pentomino