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 P pentomino

Prime rectangles: 21.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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
0
2
0
0
3
0
0
8
4
0
0
0
0
5
0
0
0
0
32
6
0
0
72
20
480
≥1000
7
0
0
4
88
2688
≥1000
≥1000
8
0
0
0
312
12420
≥1000
≥1000
≥1000
9
0
8
656
1160
55676
≥1000
≥1000
≥1000
≥1000
10
0
0
80
3336
215490
≥1000
≥1000
≥1000
≥1000
≥1000
11
0
0
80
10832
928600
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
12
0
0
5984
30326
3871934
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
13
0
24
1136
90924
17329592
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
14
0
24
1160
255354
76195732
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
15
0
0
54640
756490
341915268
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
16
0
0
14080
2159786
1.51718228×10¹⁰
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
17
0
64
14768
6403942
6.75769643×10¹⁰
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
18
0
96
499424
18519118
2.99127256×10¹¹
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
64
163056
54677936
1.32100628×10¹²
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
0
175232
158728364
5.81806789×10¹²
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
160
4569616
465484504
2.55917511×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
22
0
320
1804016
1.35059833×10¹⁰
1.12652323×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
23
0
320
1989680
3.94051790×10¹⁰
4.96376345×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
24
0
160
41855488
1.14309933×10¹¹
2.19071441×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
25
0
384
19374464
3.32778116×10¹¹
9.67500107×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
26
0
960
21919872
9.66174860×10¹¹
4.27399256×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
27
0
1280
383798144
2.81151822×10¹²
1.88729425×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
28
0
960
203668064
8.17091269×10¹²
8.33017651×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
29
0
1280
236223232
2.37763018×10¹³
3.67534578×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
30
0
2688
3.52319225×10¹⁰
6.91349983×10¹³
1.62137349×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
31
0
4480
2.10679801×10¹⁰
2.01140730×10¹⁴
7.15291249×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
32
0
4480
2.50326400×10¹⁰
5.84919268×10¹⁴
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
33
0
4736
3.23789538×10¹¹
1.70135616×10¹⁵
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
34
0
8064
2.15221812×10¹¹
4.94737343×10¹⁵
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
35
0
14336
2.61778192×10¹¹
1.43882054×10¹⁶
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
36
0
17920
2.97912993×10¹²
4.18391002×10¹⁶
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
37
0
18944
2.17678177×10¹²
1.21672729×10¹⁷
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
38
0
25600
2.70832285×10¹²
3.53820116×10¹⁷
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
39
0
45056
2.74423955×10¹³
1.02895082×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
all
40
0
64512
2.18382230×10¹³
2.99224835×10¹⁸
≥1.84467440×10²⁰
≥1
≥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
all

See Also

L tetromino and N pentominoL tetromino and R pentomino