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.


Monominoes and I pentomino

Prime rectangles: 8.

Smallest rectangle tilings

Smallest rectangle (1x6):

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 \ h12345N>0
100
20000
3000000
400000000
50022P66P1414C6060C
622P88C2626C8080C364364Call
733P1515C6363C255255C17851785Call
844P2424C124124C624624C70027002Call
955P3535C215215C12951295C2341523415Call
1066P6262C510510C40944094C8598885988Call
11≥1≥1P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
12≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0allallallallall

See Also

Monominoes and Z tetrominoMonominoes and L pentomino