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.


R pentomino and C hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (5x8):

Smallest square (14x14):

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 \ h1-456-78910111213141516N>0
1-40
5000
6-70000
8022000
90000000
10000044000
110000000000
12000000000000
1300000000000000
140000000000000022
15000088000000000000
16044000016160000000646400
17000000000000161640400000?
1800000000000000008800?
1900000000000000000000?
20000016160000003232161688???
21000000000000000000???
22000000000000000000???
230000000000000013613600???
24088000064640000000544544???
250000323200003434448448112112?????
260000000000886464144144?????
2700000000000000≥52≥52?????
280000000000512512512512???????
29000000000016169696???????
3000006464000022352352???????
31000000000000384384???????
32016160000256256044≥240≥240???????
33000000000000?????????
340000000000108108?????????
3500001281280000264264?????????
360000000000160160?????????
370000000000304304?????????
380000000000310310?????????
390000000000144144?????????
400323202562560102410240560560?????????
N>0x?x?x?x?????

See Also

R pentomino and B hexominoR pentomino and D hexomino