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 W pentomino

Prime rectangles: ≥ 30.

Smallest rectangle tilings

Smallest rectangle (4x7):

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 \ h1-345678910N>0
1-30
4000
500000
60000000
7022P0000100100P
800022P004040C222222P
90000022P4040P344344P24282428P
1002222P1212P1616P35883588P61106110C1638216382C≥400000≥400000C
11044P3434P6868P≥1≥1C1581215812C9355493554C≥1≥1Call
1200088P200200P≥1≥1C4201242012C481484481484C≥1≥1Call
130160160P202202P708708P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1405858C382382P25142514P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
15088P218218P69946994P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
160984984P22402240C2018820188P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170524524C36383638P6208462084P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
180144144C33483348C169648169648C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
19055645564P2089220892C458392458392C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
20038383838C3207032070C≥370000≥370000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

See Also

I triomino and V pentominoI triomino and X pentomino