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 and X pentomino

Prime rectangles: ≥ 40.

Smallest rectangle tilings

Smallest rectangle (10x15):

Smallest square (15x15):

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
1-9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-9
0
10
0
0
11
0
0
0
12
0
0
0
0
13
0
0
0
2
0
14
0
0
0
4
0
0
15
0
20
44
78
65022
208626
1055692
16
0
0
0
734
0
0
102743210
0
17
0
0
0
2724
0
0
472585290
0
0
18
0
4408
12216
31702
69543388
279098942
2.57847869×10¹⁰
5.13627770×10¹²
2.97480419×10¹³
2.71345553×10¹⁴
19
0
0
0
226954
0
0
1.21660043×10¹²
0
0
2.74372199×10¹⁶
0
20
0
0
0
1074444
0
0
7.41149698×10¹²
0
0
2.13750910×10¹⁷
0
0
21
0
595512
2182092
9386370
4.41220459×10¹¹
2.30772551×10¹²
4.42919412×10¹³
1.48511557×10¹⁶
1.12527326×10¹⁷
1.97429946×10¹⁸
?
≥1
all
22
0
0
0
64266592
0
0
1.26740311×10¹⁵
0
0
1.24577070×10²⁰
0
0
3k
23
0
0
0
342671958
0
0
9.51765962×10¹⁵
0
0
≥1.84467440×10²⁰
0
0
3k
24
0
65841180
329850404
2.54686663×10¹⁰
2.21673460×10¹⁴
1.56524935×10¹⁵
6.35099437×10¹⁶
3.32469142×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
25
0
0
0
1.71261624×10¹¹
0
0
1.25795197×10¹⁸
0
0
≥1.84467440×10²⁰
0
0
3k
26
0
0
0
9.77850917×10¹¹
0
0
1.09072081×10¹⁹
0
0
≥1.84467440×10²⁰
0
0
3k
27
0
6.59153091×10¹⁰
4.60122526×10¹¹
6.65590737×10¹²
9.83249064×10¹⁶
9.61769092×10¹⁷
8.07171687×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
28
0
0
0
4.39360338×10¹³
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
29
0
0
0
2.61075501×10¹⁴
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
30
0
6.23891048×10¹²
6.12683086×10¹³
1.69632839×10¹⁵
4.05142576×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
31
0
0
0
1.09976517×10¹⁶
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
32
0
0
0
6.68060598×10¹⁶
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
33
0
5.69920168×10¹⁴
7.91150192×10¹⁵
4.23669192×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
34
0
0
0
2.70531198×10¹⁸
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
35
0
0
0
1.66164482×10¹⁹
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
36
0
5.07978943×10¹⁶
9.99333753×10¹⁷
1.04041084×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
37
0
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
38
0
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
39
0
4.44623642×10¹⁸
1.24144363×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
40
0
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
41
0
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
≥1.84467440×10²⁰
0
0
3k
42
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
all
N>0
x
3k
3k
all
3k
3k
all
3k
3k
all
3k
3k

See Also

I triomino and W pentominoI triomino and Y pentomino