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 I tetromino

Prime rectangles: 19.

Smallest rectangle tilings

Smallest rectangle (2x7):

Smallest square (4x4):

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
0
0
4
0
0
0
16
5
0
0
0
32
80
6
0
0
6
48
124
≥1
7
0
6
0
224
408
≥1
≥1
8
0
0
20
680
3942
≥1
≥1
≥1
9
0
0
0
1528
14204
≥1
≥1
≥1
≥1
10
0
20
76
4344
51298
≥1
≥1
≥1
≥1
≥1
11
0
12
48
12064
162704
≥1
≥1
≥1
≥1
≥1
≥1
12
0
0
356
32576
719720
≥1
≥1
≥1
≥1
≥1
≥1
≥1
13
0
56
384
89226
2953008
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
14
0
60
1492
244212
11401772
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
15
0
20
2064
666990
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
144
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
224
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
140
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
382
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
720
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
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all
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See Also

I triomino and I heptominoL triomino and L tetromino