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.


Z pentomino and I hexomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (12x13):

Smallest square (18x18):

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 \ h1-89101112131415161718N>0
1-80
9000
1000000
110000000
12000000000
1300000002200
140000000440000
15000000066000000
1600000008800000000
17000000010100000000000
1800000001212308308≥1≥1≥1≥1≥1≥1≥1≥1≥100≥100
19000000015615600000000??≥1≥1?
20000000034334300000000??≥1≥1?
21000000057857800000000??≥1≥1?
22000000086986900000000??≥1≥1?
23000000012241224000000????≥1≥1?
24022446616591659≥5000≥5000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
250000000≥5000≥500000????????≥1≥1?
260000000≥5000≥500000????????≥1≥1?
270000000≥5000≥50000000??????≥1≥1?
280000000≥5000≥5000??????????≥1≥1?
290000000≥5000≥5000??????????≥1≥1?
3006262132132210210≥5000≥5000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
310000000≥5000≥5000??????????≥1≥1?
320000000≥5000≥5000??????????≥1≥1?
330000000≥5000≥5000??????????≥1≥1?
340000000≥5000≥5000??????????≥1≥1?
350000000≥5000≥5000??????????≥1≥1?
360111211122564256443924392≥5000≥5000≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
3700000??≥1≥1??????????≥1≥1?
3800000??≥1≥1??????????≥1≥1?
3900000??≥1≥1??????????≥1≥1?
4000000??≥1≥1??????????≥1≥1?
41000????≥1≥1??????????≥1≥1?
420≥100≥100≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
43000????≥1≥1??????????≥1≥1?
44000????≥1≥1??????????≥1≥1?
45000????≥1≥1??????????≥1≥1?
46000????≥1≥1??????????≥1≥1?
47000????≥1≥1??????????≥1≥1?
480≥100≥100≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
N>0x??????????

See Also

Z pentomino and G hexominoZ pentomino and J hexomino