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 T pentomino

Prime rectangles: ≥ 31.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

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 \ h1-23456789101112N>0
1-20
3000
400000
50000000
6011P000022C
700000001212P00
800000000022P88P
9000000033C44P1616P00
10033P0022P3535C224224P3838C414414C≥1000≥1000C
110000000107107P00120120P284284P≥1000≥1000C576576P
12011C22P33P99C250250C868868C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C
1300044P007474C7676P≥1000≥1000C732732C≥1000≥1000C≥1≥1C≥1≥1Call
14066P66P2626P394394C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
1500088P00880880C120120C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
16055C2020P3939P225225C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
170003636P00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
1801111C5656P220220P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
190008080P00≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
2001515C138138P353353C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1Call
21000224224P00??????????????all
2202222C344344P15821582C??????????????all
23000504504P00??????????????all
2403636C≥1≥1C26922692C??????????????all
25000≥1≥1C00??????????????all
2604949C≥1≥1C1053610536C??????????????all
27000≥1≥1C00??????????????all
2807979C≥1≥1C1878518785C??????????????all
29000≥1≥1C00??????????????all
300113113C≥1≥1C6723867238C??????????????all
N>0x?all?allallallallallallall

See Also

I tetromino and R pentominoI tetromino and U pentomino