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 pentomino and U pentomino

Prime rectangles: 5.

Smallest rectangle tilings

Smallest rectangle (4x5):

Smallest square (10x10):

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
1-3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-3
0
4
0
0
5
0
6
0
6
0
0
26
0
7
0
0
0
0
0
8
0
0
116
0
0
0
9
0
0
0
0
0
0
0
10
0
92
456
1342
5408
23322
150994
714516
11
0
0
0
0
0
0
0
2749892
0
12
0
0
1772
0
0
0
0
12391340
0
0
13
0
0
0
0
0
0
0
54817352
0
0
0
14
0
0
6736
0
0
0
0
285933932
0
0
0
0
15
0
1098
0
60888
141408
4510476
36097524
1.28391415×10¹⁰
≥1000
≥1000
≥1000
≥1000
≥1000
16
0
0
25464
0
0
0
0
5.74813755×10¹⁰
0
0
0
0
≥1000
0
17
0
0
0
0
0
0
0
2.58328832×10¹¹
0
0
0
0
≥1000
0
0
18
0
0
95784
0
0
0
0
1.20292282×10¹²
0
0
0
0
≥1000
0
0
0
19
0
0
0
0
0
0
0
5.71919754×10¹²
0
0
0
0
≥1000
0
0
0
0
20
0
12248
359616
2769562
50043932
913602756
4.53134169×10¹¹
2.63532870×10¹³
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
0
0
0
1.20864790×10¹⁴
0
0
0
0
≥1000
0
0
0
0
≥1
5k
22
0
0
1348448
0
0
0
0
5.56800503×10¹⁴
0
0
0
0
≥1000
0
0
0
0
≥1
5k
23
0
0
0
0
0
0
0
2.59502745×10¹⁵
0
0
0
0
≥1000
0
0
0
0
≥1
5k
24
0
0
5053328
0
0
0
0
1.21505098×10¹⁶
0
0
0
0
≥1000
0
0
0
0
≥1
5k
25
0
133528
0
128733982
2.51230579×10¹⁰
1.93857164×10¹²
2.08451550×10¹⁴
5.63968256×10¹⁶
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
all
26
0
0
18930912
0
0
0
0
2.61689288×10¹⁷
0
0
0
0
≥1
0
0
0
0
≥1
5k
27
0
0
0
0
0
0
0
1.21585766×10¹⁸
0
0
0
0
≥1
0
0
0
0
≥1
5k
28
0
0
70907360
0
0
0
0
5.67471246×10¹⁸
0
0
0
0
≥1
0
0
0
0
≥1
5k
29
0
0
0
0
0
0
0
2.64967360×10¹⁹
0
0
0
0
≥1
0
0
0
0
≥1
5k
30
0
1443780
265564192
6.11570467×10¹⁰
4.79379819×10¹²
4.27802260×10¹⁴
1.66295305×10¹⁷
1.23505094×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
5k
?
5k
5k
5k
5k
all
5k
5k
5k
5k
all
5k
5k
5k
5k
all

See Also

L pentomino and T pentominoL pentomino and V pentomino