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 pentomino

Prime rectangles: ≥ 24.

Smallest rectangle tilings

Smallest rectangle (6x7):

Smallest square (7x7):

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 \ h1-4567891011N>0
1-40
5000
600000
700044P44P
80001414P88P00
9066P3636P478478P22482248P1032810328P
10000126126P232232P13101310P6079060790C7219272192P
11022P378378P556556P20102010P271586271586C392026392026C≥1≥1C
1208080P984984P1948819488C136100136100C≥1≥1C≥1≥1C≥1≥1Call
1300027222722P83768376C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1403232P74547454C2215622156C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
150738738P1928419284C596730596730C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
160005007650076C254662254662C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170348348P130462130462C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
18058645864C332752332752C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1901616P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
20031763176C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2104301443014C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
220360360C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2302616026160C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
240300468300468C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
25049944994C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
260201718201718C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
27020320282032028C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

Smallest prime reptiles

Smallest prime reptiles (3Ix5, 5Zx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino0000738P332752P
Z pentomino02P01570P2914271P≥1P

Smallest common multiples

Smallest known common multiple (area 30):

Common multiples' solutions count (excluding symmetric)

area1530
solutions?≥1

See Also

I triomino and Y pentominoI triomino and T1 hexomino