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.


V pentomino and C hexomino

Prime rectangles: ≥ 27.

Smallest rectangle tilings

Smallest rectangle (8x19):

Smallest square (22x22):

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 \ h1-789-13141516171819202122N>0
1-70
8000
9-130000
14000000
1500000000
160000000000
17000000000000
1800000000000000
19022P0000044C000000
20000000000000000000
210000000000000000??00
220000000066P000000????22P
230000000000000000???????
240000000000000088C???????
250000000000000000???????
2600000000000022P00???????
270000000000000000???????
280000000000000022P???????
290000000000000000???????
300000000000000000???????
310000000000000000???????
32000000000000001616C???????
330000000000000000???????
340000000000000000???????
350000000000000000???????
36000022P0000000088C???????
370000000000000044P???????
38044C000001616C44P0000???????
3900000000000000?????????
40000000003232P0000?????????
41000000004848C0000?????????
4200000000000000?????????
43000000003232P0000?????????
44000022P004444C0022P?????????
45000000003232P0000?????????
46000000001414P0000?????????
4700000000000000?????????
48000000002020P0000?????????
4900000000000022P?????????
50000000002626P0000?????????
51000000001616P0088P?????????
5200000000000044C?????????
5300000000000000?????????
54000000001212P0066P?????????
5500000000000000?????????
56000000005252P00???????????
57088C000009696C00???????????
580000000088P00???????????
5900000000264264C00???????????
6000000000312312C?????????????
6100000000512512P?????????????
6200000000≥1≥1C?????????????
6300000000≥1≥1C?????????????
6400000000≥1≥1C?????????????
6500000000≥1≥1C?????????????
6600000000≥1≥1C?????????????
6700000000≥1≥1C?????????????
6800000000≥1≥1C?????????????
6900000000≥1≥1C?????????????
7000000000≥1≥1C?????????????
7100000000≥8≥8P?????????????
72000066C00≥1≥1C?????????????
7300000000≥1≥1C?????????????
7400000000≥2≥2P?????????????
7500000000≥1≥1C?????????????
7601616C00000≥1≥1C≥1≥1C???????????
7700000000≥1≥1C?????????????
7800000022P≥1≥1C?????????????
7900000000≥1≥1C?????????????
80000088C00≥1≥1C?????????????
N>0x?x??all??????

See Also

V pentomino and B hexominoV pentomino and D hexomino