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.


I tetromino, T tetromino and X pentomino

Prime rectangles: ≥ 47.

Smallest rectangle tilings

Smallest rectangle (5x9):

Smallest square (9x9):

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 \ h1-234567891011121314N>0
1-20
3000
400000
50000000
6000000000
700000000000
80000000000000
9000001414P0000002914429144P
100000022P001010P0076447644C5454C
1100000002828P412412P6363P≥1000≥1000P≥1000≥1000P≥100≥100P
1200000000044P276276P≥1000≥1000P≥1000≥1000C≥100≥100C≥100≥100P
1300000784784P154154P524524P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C
1400000178178P00≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C≥1≥1C
15000001616P37503750P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C≥1≥1Call
160000022P4646P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C≥1≥1Call
17000002971029710P2417624176P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C≥1≥1Call
180000098449844C382382P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥100≥100C≥1≥1C≥1≥1Call
190000018261826C337212337212P≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥1≥1C≥1≥1C≥1≥1Call
2000000312312C1428814288P≥1000≥1000C≥1000≥1000P≥1000≥1000C≥1000≥1000C≥100≥100C≥1≥1C≥1≥1C≥1≥1Call
2100000957260957260P≥1000000≥1000000P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2200000431074431074C100118100118C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2300000121172121172C≥1000000≥1000000P≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
24000002712227122C≥1≥1C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2500000≥1000000≥1000000C≥1≥1P≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2600000≥1000000≥1000000C≥1≥1C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x??allallallallallallallallallall

Smallest prime reptiles

Smallest prime reptile (4Ix5):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I tetromino?????P
T tetromino?????
X pentomino?????

See Also

I triomino, T tetromino and X pentominoI tetromino, X pentomino and Z pentomino