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 L tetromino

Prime rectangles: 16.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (4x4):

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 \ h1234567N>0
10
2000
300000
40000088P
50001212P3838P156156P
60002828P188188P14901490C1092010920C
7066P5656P616616C66086608C8262082620C908682908682C
8000136136P20682068C2460624606C601870601870C≥1≥1Call
9000266266P75967596C162180162180C≥1≥1C≥1≥1Call
1001212P668668C2468024680C≥1≥1C≥1≥1C≥1≥1Call
1102020P15781578C8366883668C≥1≥1C≥1≥1C≥1≥1Call
1200033703370C288718288718C≥1≥1C≥1≥1C≥1≥1Call
1302020P78607860C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1406060C1690216902C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1505656P3741837418C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1603030P8498084980C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170140140C185864185864C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
180224224C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
190186186P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
200280280C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
210672672C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
220776776C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
230856856C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
24016801680C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
25027122712C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
26029522952C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
27045284528C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
28080108010C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2901047210472C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
3001321613216C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
3102262222622C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
3203401234012C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallall

Smallest prime reptiles

Smallest prime reptiles (3Ix3, 4Lx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino00266P288718P
L tetromino03P3247P31237237C

Smallest common multiples

Smallest common multiple (area 12):

Common multiples' solutions count (excluding symmetric)

area12
solutions≥1P

See Also

I triomino and I tetrominoI triomino and O tetromino