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.


I triomino, T tetromino and X pentomino

Prime rectangles: 26.

Smallest rectangle tilings

Smallest rectangle (3x9):

Smallest square (7x7):

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
1-2
0
3
0
0
4
0
0
0
5
0
0
0
0
6
0
0
0
0
0
7
0
0
2
4
12
370
8
0
0
8
0
96
3112
4974
9
0
4
14
54
1296
12132
105848
≥1
10
0
8
56
196
4550
106622
≥250000
≥1
≥1
11
0
12
150
113
19538
≥250000
≥250000
≥1
≥1
≥1
12
0
40
310
2052
128888
≥250000
≥250000
≥1
≥1
≥1
≥1
13
0
84
970
7232
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
14
0
152
2404
9998
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
≥1
15
0
328
5352
61204
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
16
0
680
14244
231116
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
1300
35186
≥250000
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
2504
79886
≥250000
≥250000
≥250000
≥250000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
?
?

Smallest prime reptiles

Smallest prime reptiles (3Ix3, 4Tx3, 5Xx3):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino
0
0
4
310
61204
T tetromino
0
0
8
5274
1062492
X pentomino
0
0
32
147740
≥90000

See Also

Monominoes, Dominoes and I triominoI tetromino, T tetromino and X pentomino