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, Dominoes and I triomino

Prime rectangles: 10.

Smallest rectangle tilings

Smallest rectangles (1x6, 2x3):

Smallest square (3x3):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - 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 \ h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
0
2
0
0
3
0
4
100
4
0
28
1214
27100
5
0
166
12182
552079
≥1
6
6
812
113956
10704644
≥1
≥1
7
12
3630
1020254
201350498
≥1
≥1
≥1
8
32
15532
8926506
3.72839620×10¹⁰
≥1
≥1
≥1
≥1
9
72
64520
76952804
6.83571751×10¹¹
≥1
≥1
≥1
≥1
≥1
10
152
262750
656821346
1.24524100×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
11
311
1055529
5.56791685×10¹⁰
2.25910053×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
12
625
4198067
4.69703041×10¹¹
4.08731379×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
all
all
all
all
all
all
all
all
all
all
all
all
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See Also

T1 hexomino and I 9-ominoI triomino, T tetromino and X pentomino