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.


T tetromino and A hexomino

Prime rectangles: ≥ 16.

Smallest rectangle tilings

Smallest rectangle (4x7):

Smallest square (8x8):

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 \ h1-345678910111213N>0
1-30
4000
500000
60000000
701212P00000
80000000332332C224224P
9000000003636P0
1004040P0000128128P≥1000≥1000C760760P228228P
1105252P00000≥1000≥1000C0≥1000≥1000C0
120000000≥1000≥1000C≥1000≥1000P≥1000≥1000P≥1000≥1000C≥1000≥1000C≥1000≥1000P
130112112P00000≥1000≥1000C0≥1000≥1000C0≥1000≥1000C0
140248248C0000≥1000≥1000C≥1000≥1000C≥1000≥1000P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
150204204P00000≥1000≥1000C0≥1000≥1000C0≥1000≥1000C02k
160288288P0000≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
170912912C00000≥1≥1C0≥1≥1C0≥1≥1C02k
180≥1000≥1000C0000≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
190≥1000≥1000P00000≥1≥1C0≥1≥1C0≥1≥1C02k
200≥1000≥1000C0000≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xall??2kall2kall2kall2k

See Also

T tetromino and Z pentominoT tetromino and B hexomino