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 T1 hexomino

Prime rectangles: ≥ 17.

Smallest rectangle tilings

Smallest known rectangle and smallest square (12x12):

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 \ h1234567891011121314
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
1000000000000000000000
110000000000000000000000
12000000000000000000000022P
1300000000000000000000000000
14000000000000000000000022P0000
1500000000000000000000008080P0000
160000000000000000000022P6666P890890P558558P
170000000000000000000000778778P00??
180000000000000000000000≥1000≥1000P00??
19????????????????????00≥1≥1P????
20????????????????????≥1≥1P≥1≥1P????
21????????????????????00≥1≥1P????
22????????????????????00≥1≥1P????
23????????????????????00≥1≥1P????
24????????????????????≥1≥1P≥1≥1C????
25????????????????????00≥1≥1P????
26??????????????????????≥1≥1C????
27??????????????????????≥1≥1C????

See Also

Z tetromino and P hexominoZ tetromino and T2 hexomino