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 tetromino and U pentomino

Prime rectangles: 27.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

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
N>0
1-2
0
3
0
0
4
0
0
0
5
0
0
0
0
6
0
2
0
40
8
7
0
0
0
32
240
4456
8
0
0
0
24
212
1132
20268
9
0
4
0
1416
6452
32476
167056
1850160
10
0
0
0
2644
4774
255302
1540678
52654914
≥1
11
0
8
32
2880
60092
514004
10813998
354597420
≥1
≥1
12
0
12
0
3982
76124
3722908
91525660
2.64618813×10¹⁰
≥1
≥1
≥1
13
0
0
194
7812
1316178
33615444
686978150
4.43550306×10¹¹
≥1
≥1
≥1
≥1
14
0
36
100
68830
1645968
249776778
5.18631125×10¹⁰
2.70298741×10¹²
≥1
≥1
≥1
≥1
≥1
15
0
32
1326
245492
13073842
1.19990721×10¹⁰
3.76692492×10¹¹
3.01454974×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
16
0
0
640
575190
26146090
3.22232823×10¹⁰
2.75197515×10¹²
2.32863970×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
17
0
112
8142
3403108
257426040
2.01985073×10¹¹
1.97029716×10¹³
2.02214385×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
88
4480
9870846
475844036
9.06482984×10¹¹
1.40097182×10¹⁴
2.57528839×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
96
46054
22579032
2.69868366×10¹⁰
4.45644370×10¹²
9.91200121×10¹⁴
1.98707056×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
368
27608
43066544
7.07212217×10¹⁰
2.92779075×10¹³
6.94653072×10¹⁵
1.94353682×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
240
251836
79408160
4.96240392×10¹¹
1.74559431×10¹⁴
4.86513161×10¹⁶
1.91128322×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
456
158888
225937332
1.17916416×10¹²
9.06705860×10¹⁴
3.38374206×10¹⁷
1.55461888×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
1152
1332130
787520880
5.50031377×10¹²
4.24381827×10¹⁵
2.35427167×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
656
878336
2.46635016×10¹⁰
1.68531005×10¹³
1.80828219×10¹⁶
1.62869146×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
1776
6879496
9.89072001×10¹⁰
9.56705024×10¹³
9.14872471×10¹⁶
1.12808192×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
3568
4703068
3.05899861×10¹¹
2.66884131×10¹⁴
4.64547205×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
2656
34851150
8.40434437×10¹¹
1.11878385×10¹⁵
2.55417309×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
0
6672
24597312
2.07505905×10¹²
3.74014759×10¹⁵
1.41210131×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
29
0
10880
173856702
4.72188952×10¹²
1.85516023×10¹⁶
7.34799410×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
30
0
9648
126238472
1.11548171×10¹³
5.73325244×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
N>0
x
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all
all

Smallest prime reptiles

Smallest prime reptiles (4Lx3, 5Ux4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
L tetromino
0
0
4
2123
≥1
≥1
≥1
U pentomino
0
0
0
69701
≥1
≥1
≥1

Smallest common multiples

Smallest common multiple (area 20):

Common multiples' solutions count (excluding symmetric)

area
20
solutions
≥2

See Also

L tetromino and T pentominoL tetromino and V pentomino