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 triomino and Z tetromino

Prime rectangles: ≥ 29.

Smallest rectangle tilings

Smallest rectangles and smallest square (4x9, 6x6):

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 \ h1-3456789N>0
1-30
4000
500000
60000044P
7000003434P00
80004040P8484P320320P82048204P
901616P5454P370370P47504750P2760227602C≥1≥1C
100001212P14461446P33463346P8483284832C≥1≥1Call
11088P756756P43744374P4311443114P11845541184554C≥1≥1Call
120188188P10621062P1545815458C361460361460C≥1≥1C≥1≥1Call
13022P472472P≥5000≥5000C≥5000≥5000P≥1≥1C≥1≥1Call
140112112P≥5000≥5000P≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
15016001600P≥5000≥5000P≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
1607474P≥5000≥5000C≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
17012421242P≥5000≥5000C≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
180≥5000≥5000C≥5000≥5000C≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
19013641364P≥5000≥5000C≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
200≥5000≥5000C≥5000≥5000C≥5000≥5000C≥5000≥5000C≥1≥1C≥1≥1Call
N>0xallallallallallall

See Also

I triomino and T tetrominoI triomino and I pentomino