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 X2 hexomino

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle (13x31):

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 \ h1-121314-1617181920N>0
1-120
13000
14-160000
17000000
1800000000
190000000000
20000000000000
21000000000000?
22000000000000?
2300000000?????
2400000000?????
2500000000?????
2600000000?????
2700000000?????
2800000000?????
29000000≥1≥1?????
3000002200?????
31022P00000?????
3200000000?????
3300000000?????
3400000000?????
3500000000?????
3600000000?????
3700000000?????
38000000≥1≥1?????
3900000000?????
4000000000?????
4100000000?????
4200000000?????
4300000000?????
4400000000?????
4500000000?????
46000000≥1≥1?????
47000000≥1≥1?????
4800000000?????
4900000000?????
5000000000?????
5100000000?????
52000044≥1≥1?????
5300000000?????
5400000000?????
55000000≥1≥1?????
5600000000?????
5700000000?????
58000000≥1≥1?????
59000000≥1≥1?????
60000044≥1≥1?????
61000000≥1≥1?????
62044C00000?????
63000000≥1≥1?????
64000000≥1≥1?????
65000000≥1≥1?????
66000022≥1≥1?????
67000000≥1≥1?????
68000000≥1≥1?????
69000000≥1≥1?????
70000044≥1≥1?????
71000000≥1≥1?????
72000000≥1≥1?????
73000044≥1≥1?????
74000000≥1≥1?????
75000000≥1≥1?????
76000044≥1≥1?????
77000088≥1≥1?????
78000000≥1≥1?????
79000044≥1≥1?????
80000044≥1≥1?????
81000088≥1≥1?????
8200001616≥1≥1?????
83000088≥1≥1?????
84000044≥1≥1?????
85000000≥1≥1?????
86000066≥1≥1?????
87000044≥1≥1?????
88000066≥1≥1?????
8900001212≥1≥1?????
9000002828≥1≥1?????
9100002424≥1≥1?????
9200001010≥1≥1?????
93088C01616???????
9400004444???????
9500002222???????
9600003838???????
9700005858???????
9800006868???????
9900005656???????
10000005050???????
N>0x?x????

See Also

U pentomino and V2 hexominoU pentomino and Y1 hexomino