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.


U pentomino and Y pentomino

Prime rectangles: ≥ 38.

Smallest rectangle tilings

Smallest known rectangle (3x10):

Smallest square (10x10):

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 \ h12345678910
100
2??00
3????00
4????0000
5????000000
6????00000000
7????0000000000
8????000000000000
9????00000000000000
10????22P0010102222363618018081081033703370
11????000012120000000077107710
12????00004400000000≥1≥1
13????00008800000000≥1≥1
14????0000565600000000≥1≥1
15????002240406060736736901690168657286572≥1≥1
16????0000181800000000≥1≥1
17????0000242400000000≥1≥1
18????0000646400000000≥1≥1
19????000010010000000000≥1≥1
20????4422418418138213822175621756≥1≥1≥1≥1≥1≥1

Smallest prime reptiles

Smallest prime reptiles (5Ux4, 5Yx4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
U pentomino0002192676235≥16000
Y pentomino0001130383587≥350000

See Also

U pentomino and X pentominoU pentomino and A hexomino