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.


T tetromino and X pentomino

Prime rectangles: ≥ 51.

Smallest rectangle tilings

Smallest known rectangle and smallest square (11x11):

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
1000000000000000000000
110000000000000000000022
12000000000000000000000000
1300000000000000000000000000
140000000000000000000000880000
150000000000000000000000100100000065926592
160000000000000000000000000015361536??
17000000000000000000000000??3232??
18000000000000000000000048004800??????
1900000000000000000000002420824208??????
20000000000000000000000013521352??????
21000000000000000000003232320320??????
22000000000000000000003434≥1≥1??????
2300000000000000000000574574≥1≥1??????
2400000000000000000000960960≥1≥1??????
2500000000000000000000792792≥1≥1??????
2600000000000000880000≥1000≥1000≥1≥1??????
2700000000000000000000≥1000≥1000≥1≥1??????
2800000000000000000000≥1000≥1000≥1≥1??????
2900000000000000000000≥1000≥1000≥1≥1??????
30000000000000003523520000≥1000≥1000≥1≥1??????
31??????????????≥1≥1????≥1≥1≥1≥1??????
32??????????????00????≥1≥1≥1≥1??????
33??????????????00????≥1≥1≥1≥1??????
34??????????????≥1≥1??????????????
35??????????????≥1≥1??????????????
36??????????????????????????????
37??????????????????????????????
38??????????????≥1≥1??????????????
39??????????????≥1≥1??????????????
40??????????????????????????????
41??????????????????????????????
42??????????????≥1≥1??????????????
43??????????????≥1≥1??????????????
44??????????????????????????????
45??????????????????????????????
46??????????????≥1≥1??????????????
47??????????????≥1≥1??????????????
48??????????????????????????????
49??????????????????????????????
50??????????????≥1≥1??????????????
51??????????????≥1≥1??????????????
52??????????????≥1≥1??????????????
53??????????????????????????????
54??????????????≥1≥1??????????????
55??????????????≥1≥1??????????????

See Also

T tetromino and W pentominoT tetromino and Y pentomino