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.


L triomino and X pentomino

Prime rectangles: ≥ 37.

Smallest rectangle tilings

Smallest rectangle (5x7):

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
70009696P00130130P
800022P0045524552P30723072P
9000000012881288P1260012600P117152117152P
10000400400P004930649306C≥1000≥1000C18810541881054P≥1000≥1000C
11088P160160P00456640456640P≥1000≥1000C≥1000≥1000C≥1000≥1000Call
120003232P536536P259822259822C≥1000≥1000C≥1000≥1000P≥1000≥1000Call
13022P1817618176P12761276P44405764440576C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
140144144P1162411624C1159611596P≥1≥1C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1500010241024C5516455164P≥1≥1C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1606868P≥1000≥1000C241928241928P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
17017281728P≥1000≥1000C11590761159076P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1801616P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
19012001200P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2001728217282P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
210512512P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2201590415904C≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
230155888155888P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
240≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
250≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
260≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
270≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

See Also

L triomino and W pentominoL triomino and Y pentomino