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.


N pentomino, T pentomino and X pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (5x14):

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 \ h12345678910111213141516171819
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
100000000000000000≥1≥1≥1≥1
11000000000000000000≥1≥100
12000000000000000000≥1≥10000
13000000000000000000≥1≥1000000
1400000000≥1≥100000000≥1≥100000000
1500000000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
16000000000000000000≥1≥100000000≥1≥100
1700000000≥1≥100000000≥1≥100000000≥1≥10000
1800000000≥1≥100000000≥1≥100000000≥1≥1000000
19000000000000000000≥1≥100000000≥1≥100000000
2000000000≥1≥100≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1
2100000000≥1≥100000000≥1≥100000000≥1≥100000000
2200000000≥1≥100000000≥1≥100000000≥1≥100000000
2300000000≥1≥100000000≥1≥100000000≥1≥100000000
2400000000≥1≥100000000≥1≥100000000≥1≥100000000
2500000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
2600000000≥1≥100000000≥1≥100000000≥1≥1000000??
2700000000≥1≥100000000≥1≥100000000≥1≥1000000??
2800000000≥1≥100000000≥1≥100000000≥1≥1000000??
2900000000≥1≥100000000≥1≥100000000≥1≥1000000??
3000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
3100000000≥1≥100000000≥1≥100000000≥1≥1000000??
3200000000≥1≥100000000≥1≥100000000≥1≥1000000??
3300000000≥1≥100000000≥1≥100000000≥1≥1000000??
3400000000≥1≥100000000≥1≥100000000≥1≥1000000??
3500000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
3600000000≥1≥100000000≥1≥100000000≥1≥1000000??
3700000000≥1≥100000000≥1≥100000000≥1≥1000000??
3800000000≥1≥100000000≥1≥100000000≥1≥1000000??
3900000000≥1≥100000000≥1≥100000000≥1≥1000000??
4000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
4100000000≥1≥100000000≥1≥100000000≥1≥1000000??
4200000000≥1≥100000000≥1≥100000000≥1≥1000000??
4300000000≥1≥100000000≥1≥100000000≥1≥1000000??
4400000000≥1≥100000000≥1≥100000000≥1≥1000000??
4500000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??
4600000000≥1≥100000000≥1≥100000000≥1≥1000000??
4700000000≥1≥100000000≥1≥100000000≥1≥1000000??
4800000000≥1≥100000000≥1≥100000000≥1≥1000000??
4900000000≥1≥100000000≥1≥100000000≥1≥1000000??
5000000000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1??

See Also

I tetromino, X pentomino and Z pentominoI tetromino, L tetromino, O tetromino and T tetromino