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 O hexomino

Prime rectangles: ≥ 32.

Smallest rectangle tilings

Smallest rectangle (7x10):

Smallest square (10x10):

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 \ h1-45678910111213141516N>0
1-40
5000
600000
7000000
8000000000
9000000000
100000022P00001616P
1100000000088P00
1200000000000000000
1300000022P07676P00242400
140000022P00005252C68682020654654848848
150000000002020P001441440088488400
16000001212P66P44P366366P334334244244≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
17000000000312312C0052652600≥1000≥100000≥1000≥1000?
180000022P001616P172172C170170≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
190000002424P0≥1000≥1000P00≥1000≥100000≥1000≥100000≥1000≥1000?
20000001616C44P4040P≥1000≥1000C≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
21000000000≥1≥1C?????????????
22000005656P8484P130130P≥1≥1C?????????????
230000001616P0≥1≥1C?????????????
24000002020C00400400P≥1≥1C?????????????
25000000292292P0≥1≥1C?????????????
26000009292C6868C≥1000≥1000P≥1≥1C?????????????
2700000088P0≥1≥1C?????????????
2800000240240C984984P≥1000≥1000P≥1≥1C?????????????
29000000252252C0≥1≥1C?????????????
3000000136136C4040P≥1000≥1000P≥1≥1C?????????????
310????0≥1000≥1000P0≥1≥1C?????????????
320????≥1≥1C912912C≥1≥1C≥1≥1C?????????????
330????0184184C0≥1≥1C?????????????
340????≥1≥1C≥1000≥1000P≥1≥1C≥1≥1C?????????????
350????0≥1000≥1000C0≥1≥1C?????????????
360????≥1≥1C728728C≥1≥1C≥1≥1C?????????????
370????0≥1000≥1000P0≥1≥1C?????????????
380????≥1≥1C≥1000≥1000C≥1≥1C≥1≥1C?????????????
390????0≥1000≥1000C0≥1≥1C?????????????
400????≥1≥1C≥1000≥1000C≥1≥1C≥1≥1C?????????????
N>0x??2kall2kall??????

See Also

U pentomino and N3 hexominoU pentomino and P hexomino