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.


U pentomino and A hexomino

Prime rectangles: ≥ 9.

Smallest rectangle tilings

Smallest rectangle (7x20):

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 \ h1-67891011121314N>0
1-60
7000
800000
90000000
10000000000
1100000000000
120000000000000
13000000000000000
1400000000000000000
150000000000000?????
160000000000000?????
170000000000000?????
180000000000000?????
19000000000≥1000≥1000P512512P?????
20020482048P0000≥1000≥1000P≥1000≥1000P????≥1≥1C?
2100000000000???????
22000000000?????????
23000000000?????????
240000000???????????
250000000???????????
260000000???????????
270000000???????????
280≥1000≥1000P0000????????≥1≥1C?
290000000???????????
3000000?????????????
3100000?????????????
320≥1000≥1000P00??????????≥1≥1C?
3300000?????????????
34000???????????????
35000???????????????
360≥1000≥1000P????????????≥1≥1C?
37000???????????????
38000??????≥1≥1C≥1≥1C?????
390????????≥1≥1C???????
400≥1≥1C????≥1≥1C≥1≥1C????≥1≥1C?
410?????????????????
420?????????????????
430?????????????????
440≥1000≥1000P????????????≥1≥1C?
450?????????????????
460?????????????????
470?????????????????
480≥1≥1C????????????≥1≥1C?
N>0x????????

See Also

U pentomino and Y pentominoU pentomino and B hexomino