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 tetromino and I pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (7x12):

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 \ h12345678910111213
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
10000000000000000000148148
1100000000000000880034034000
120000000000004444005454830830≥1000≥1000≥1000≥1000
1300000000000000484888≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
14000000000000008800≥1≥1≥1≥1????
15000000000018185252418418≥1000≥1000≥1≥1≥1≥1????
160000000000000032632600≥1≥1??????
17000000000000≥1000≥1000≥1000≥1000≥1000≥1000≥1≥1??????
1800000000000000≥1000≥1000≥1000≥1000≥1≥1??????
19000000000000400400≥1000≥1000??≥1≥1??????
200000000000300300≥1000≥1000≥1000≥1000??≥1≥1??????

See Also

T tetromino and Z2 hexominoZ tetromino and L pentomino