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.


T tetromino and U pentomino

Prime rectangles: ≥ 81.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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 \ h1234567891011
100
20000
3000044
400000000
50000000000
6000016160022260260
700000000004400
8000000000068680000
900006464000042444244525222284272284272
1000000000001381388811801180104741047499709970
1100000000001692169211161116256825687327326425464254469480469480
1200002562560022693326933215978159782137821378≥1≥1≥1≥1≥1≥1
13000000003232352835285685681304813048??????
1400000000883717037170126212622240622406??????
1500001024102400001132972113297285248524≥1≥1??????
1600000000007977079770≥1≥1≥1≥1??????
170000000000763216763216≥1≥1≥1≥1??????
18000040964096001401401851963418519634≥1≥1≥1≥1??????
1900000000256256≥1≥1≥1≥1≥1≥1??????
20000000006464≥1≥1≥1≥1≥1≥1??????
21000016384163840000≥1≥1≥1≥1≥1≥1??????
220000000000≥1≥1≥1≥1≥1≥1??????
230000000028882888≥1≥1≥1≥1≥1≥1??????
2400006553665536001574015740≥1≥1≥1≥1≥1≥1??????
25000000002518425184≥1≥1≥1≥1≥1≥1??????

Smallest prime reptiles

Smallest prime reptiles (4Tx3, 5Ux3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
T tetromino00256P0162P≥4815104840P≥1P
U pentomino001024P021418P≥1251927258400P≥1P

Smallest common multiples

Smallest common multiple (area 40):

Common multiples' solutions count (excluding symmetric)

area2040
solutions?≥1

See Also

T tetromino and T pentominoT tetromino and V pentomino