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.


I tetromino and X2 hexomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest known rectangle (13x24):

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 \ h1-12131415N>0
1-120
13000
1400000
150000000
160000000?
1700000???
18000?????
19000?????
20000?????
21000?????
22000?????
23000?????
2405050P?????
25000?????
26000?????
27000?????
2802002020020P?????
29000?????
30000?????
31000?????
32045914284591428P?????
33000?????
34000?????
35000?????
360830263398830263398P?????
37000?????
38000?????
39000?????
4001.33826117×10¹²133826117020P?????
41000?????
42000?????
43000?????
4402.02900140×10¹⁴20290014003346P?????
45000?????
46000?????
47000?????
4802.96621758×10¹⁶2966217580007580C?????
49000?????
50000?????
51000?????
5204.23231835×10¹⁸423231835519293710C?????
53000?????
54000?????
55000?????
560≥1.84467440×10²⁰≥18446744073709551615C?????
N>0x???

See Also

I tetromino and T1 hexominoI tetromino and C heptomino