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 pentomino and R pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known rectangle (10x11):

Smallest square (15x15):

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 \ h123456789101112131415
100
20000
3000000
400000000
50000000000
6000000000000
700000000000000
80000000000000000
9000000000000000000
1000000000000000000000
110000000000000000002200
1200000000000000000010100000
130000000000000000001818000000
14000000000000000000303000000000
150000000000000000004242770770≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
1600000000000000000020220200000000≥1000≥1000
1700000000000000000087887800000000≥1000≥1000
18000000000000000000≥1000≥100000000000≥1000≥1000
19000000000000000000≥1000≥100000000000≥1000≥1000
20000000000022666868334334≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
21000000000000000000≥1000≥100000000000≥1000≥1000
22000000000000000000≥1000≥100000000000≥1000≥1000
23000000000000000000≥1000≥100000000000≥1000≥1000
24000000000000000000≥1000≥100000000000≥1000≥1000
2500000000004444214214≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

See Also

I pentomino and P pentominoI pentomino and T pentomino