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 tetromino and I pentomino

Prime rectangles: 22.

Smallest rectangle tilings

Smallest rectangle (1x9):

Smallest square (5x5):

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 \ h123456789N>0
100
20000
3000000
400000000
5000000001212P
600000022P2323P1616P
700000033P3434P88P00
800000044P5353P128128C214214C632632C
922P44C88C2121C215215C922922C≥1000≥1000C≥1000≥1000C≥1000≥1000C
100000004040P557557C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
110000006464P10641064C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120000009090C19161916C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1333P99C2727C200200C46464646C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1433P99C2727C428428C1196811968C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
15000000730730C2671626716C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1600000011161116C5316953169C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1744P1616C6464C18461846C113107113107C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1866C3636C216216C41644164C267707267707C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1944P1616C6464C76737673C629709629709C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
200022P66P1249412494C13596971359697C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
2155P2525C125125C1947419474C28782112878211C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
221010C100100C10001000C3894138941C64151476415147C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
231010C100100C10001000C7736777367C1488995314889953C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2455P3535C215215C134211134211C3352761733527617C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2566P4848C342342C215524215524C7281127272811272C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
261515C225225C33753375C376608376608C159321249159321249C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
272020C400400C80008000C772723772723C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
281515C255255C40954095C14284041428404C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
291313P169169C21972197C24048022404802C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
302121C483483C1064710647C40017064001706C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0allallallallallallallallall

See Also

I tetromino and Z tetrominoI tetromino and L pentomino