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, T tetromino and X pentomino

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (3x9):

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 \ h1-2345678N>0
1-20
3000
400000
50000000
6000000000
700022P44P1212P370370P
800088P009696P31123112C49744974C
9044P1414P5454P12961296C1213212132C105848105848Call
10088P5656P196196P45504550C106622106622C≥250000≥250000Call
1101212P150150P113113P1953819538C≥250000≥250000C≥250000≥250000Call
1204040P310310P20522052P128888128888C≥250000≥250000C≥250000≥250000Call
1308484P970970P72327232P≥250000≥250000C≥250000≥250000C≥250000≥250000Call
140152152P24042404C99989998C≥250000≥250000C≥250000≥250000C≥250000≥250000Call
150328328P53525352C6120461204P≥250000≥250000C≥250000≥250000C≥250000≥250000Call
160680680P1424414244C231116231116C≥250000≥250000C≥250000≥250000C≥250000≥250000Call
17013001300P3518635186C≥250000≥250000C≥250000≥250000C≥250000≥250000C≥250000≥250000Call
18025042504C7988679886C≥250000≥250000C≥250000≥250000C≥250000≥250000C≥250000≥250000Call
N>0xallallallallallall

Smallest prime reptiles

Smallest prime reptiles (3Ix3, 4Tx3, 5Xx3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino004P310P61204P
T tetromino008P5274P1062492P
X pentomino0032P147740P≥90000P

See Also

Monominoes, Dominoes and I triominoI tetromino, T tetromino and X pentomino