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 pentomino and Y2 hexomino

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest known rectangle and smallest known square (36x36):

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 \ h1-222324252627282930313233343536N>0
1-220
23000
2400000
250000000
26000000000
2700000000000
2800000000000??
2900000000000????
3000000000000??????
3100000000000????????
3200000000000??????????
3300000000000????????????
34000000000????????????????
35000000000??????????????????
36000000000??????????????????≥1≥1P
3700000?????????????????????????
3800000?????????????????????????
3900000?????????????????????????
4000000?????????????????????????
4100000?????????????????????????
4200000?????????????????????????
4300000?????????????????????????
4400000?????????????????????????
4500000?????????????????????????
4600000?????????????????????????
4700000?????????????????????????
48000???????????????????????????
49000???????????????????????????
50000???????????????????????????
51000???????????????????????????
52000???????????????????????????
53000???????????????????????????
54000???????????????????????????
55000???????????????????????????
56000???????????????????????????
N>0x??????????????

Attributions

  1. Smallest rectangle taken from here http://www2.stetson.edu/~efriedma/mathmagic/0810.html

See Also

Z pentomino and Y1 hexominoI hexomino and T1 hexomino