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.


T tetromino and Z tetromino

Prime rectangles: 7.

Smallest rectangle tilings

Smallest rectangle (4x5):

Smallest square (8x8):

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
4
0
6
0
8
0
0
7
0
18
0
0
0
8
0
38
64
192
1648
20994
9
0
104
0
0
0
108836
0
10
0
242
0
0
0
574394
0
1948648
11
0
564
0
0
0
3828798
0
0
0
12
0
1302
1216
5000
261558
27139512
202910308
2.14734763×10¹⁰
5.36061914×10¹¹
1.56032340×10¹³
13
0
3090
0
0
0
171246674
0
0
0
2.28369656×10¹⁴
0
14
0
7228
0
928
0
1.05537535×10¹⁰
0
3.05809863×10¹¹
0
3.47914510×10¹⁵
0
≥1
15
0
16904
0
0
0
6.78662211×10¹⁰
0
0
0
6.97913846×10¹⁶
0
0
0
16
0
39484
24148
134960
54811674
4.41874118×10¹¹
4.58733621×10¹²
9.42922154×10¹³
1.07323205×10¹⁶
1.45806283×10¹⁸
≥1
≥1
≥1
≥1
17
0
92484
0
0
0
2.83449698×10¹²
0
0
0
2.55228372×10¹⁹
0
0
0
≥1
0
18
0
216328
0
60512
0
1.80491985×10¹³
0
2.68407271×10¹⁵
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
19
0
506002
0
0
0
1.15698106×10¹⁴
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1
0
0
0
20
0
1183402
484632
3712920
1.27308601×10¹¹
7.43625907×10¹⁴
1.12341220×10¹⁶
4.54321320×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
2768424
0
0
0
4.77077813×10¹⁵
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1
0
0
0
≥1
?
22
0
6475506
0
2758048
0
3.05579651×10¹⁶
0
1.90583773×10¹⁹
0
≥1.84467440×10²⁰
0
≥1
0
≥1
0
≥1
0
≥1
?
23
0
15146580
0
0
0
1.95914892×10¹⁷
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1
0
0
0
≥1
?
24
0
35428226
9757806
103288088
3.04985662×10¹³
1.25673562×10¹⁸
2.85139648×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
82869778
0
0
0
8.06006413×10¹⁸
0
0
0
≥1.84467440×10²⁰
0
0
0
≥1
0
0
0
≥1
?
N>0
x
all
4k
2k
4k
all
4k
2k
4k
all
?
?
?
?
?
?
?
?

See Also

O tetromino and Z2 hexominoT tetromino and I pentomino