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.


O tetromino and N pentomino

Prime rectangles: ≥ 120.

Smallest rectangle tilings

Smallest rectangle (8x20):

Smallest square (14x14):

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
1-7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-7
0
8
0
0
9
0
0
0
10
0
0
0
0
11
0
0
0
0
0
12
0
0
0
0
0
0
13
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
2
15
0
0
0
0
0
0
0
0
?
16
0
0
0
0
0
0
0
16
?
?
17
0
0
0
0
0
0
0
20
?
?
?
18
0
0
0
0
0
4
0
472
?
?
?
?
19
0
0
0
0
0
2
0
≥260
?
?
?
?
?
20
0
1
0
3
0
199
52
≥1
?
≥1
?
≥1
?
≥1
21
0
0
0
0
0
18
0
≥1
?
?
?
?
?
≥1
?
22
0
3
0
17
0
1235
148
≥1
?
≥1
?
≥1
?
≥1
?
23
0
0
0
2
0
552
32
≥1
?
?
?
?
?
≥1
?
24
0
7
0
93
0
9364
4362
≥1
?
≥1
?
≥1
≥1
≥1
?
25
0
2
0
26
0
13430
2964
≥1
?
≥1
?
≥1
?
≥1
?
26
0
14
0
387
0
70843
65554
≥1
?
≥1
?
≥1
≥1
≥1
?
27
0
8
0
238
0
195640
132008
≥1
?
≥1
?
≥1
?
≥1
?
28
0
26
0
1918
296
657452
1084146
≥1
?
≥1
≥1
≥1
≥1
≥1
?
29
0
24
0
2244
0
2319040
3351476
≥1
?
≥1
?
≥1
?
≥1
?
30
0
58
0
9160
592
7048969
15282008
≥1
?
≥1
?
≥1
≥1
≥1
?
31
0
62
0
14782
336
25230030
58404876
≥1
?
≥1
?
≥1
≥1
≥1
?
32
0
133
0
47605
2336
79361418
224783002
≥1
?
≥1
?
≥1
≥1
≥1
?
33
0
146
0
92290
7232
270228548
898749716
≥1
?
≥1
?
≥1
≥1
≥1
?
34
0
312
0
265934
16120
891498126
3.41362636×10¹⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
35
0
354
0
549252
40048
2.93306176×10¹⁰
1.32488768×10¹¹
≥1
?
≥1
?
≥1
≥1
≥1
?
36
0
741
0
1507220
112360
9.90062310×10¹⁰
5.10733051×10¹¹
≥1
?
≥1
?
≥1
≥1
≥1
?
37
0
910
0
3216462
287152
3.22868616×10¹¹
1.93201381×10¹²
≥1
?
≥1
?
≥1
≥1
≥1
?
38
0
1792
0
8608776
721896
1.09016063×10¹²
7.52582937×10¹²
≥1
?
≥1
?
≥1
≥1
≥1
?
39
0
2446
0
18873434
2004112
3.57648780×10¹²
2.82530320×10¹³
≥1
?
≥1
?
≥1
≥1
≥1
?
40
0
4430
0
49164837
5005656
1.19759181×10¹³
1.09903556×10¹⁴
≥1
?
≥1
?
≥1
≥1
≥1
?
41
0
6658
0
110612984
13340208
3.96200967×10¹³
4.14062536×10¹⁴
≥1
?
≥1
?
≥1
≥1
≥1
?
42
0
11420
0
281222202
36024752
1.31766376×10¹⁴
1.59833753×10¹⁵
≥1
?
≥1
≥1
≥1
≥1
≥1
?
43
0
18296
0
646881282
90733424
4.37966013×10¹⁴
6.06746530×10¹⁵
≥1
?
≥1
?
≥1
≥1
≥1
?
44
0
30860
0
1.61332684×10¹⁰
244674488
1.45285061×10¹⁵
2.32488813×10¹⁶
≥1
?
≥1
?
≥1
≥1
≥1
?
45
0
50510
0
3.77000280×10¹⁰
627017392
4.83346489×10¹⁵
8.87330134×10¹⁶
≥1
?
≥1
?
≥1
≥1
≥1
?
46
0
85881
0
9.28309425×10¹⁰
1.66355302×10¹⁰
1.60364195×10¹⁶
3.38721905×10¹⁷
≥1
?
≥1
?
≥1
≥1
≥1
?
47
0
141892
0
2.19140294×10¹¹
4.34951678×10¹⁰
5.33150442×10¹⁶
1.29509433×10¹⁸
≥1
?
≥1
?
≥1
≥1
≥1
?
48
0
244269
0
5.35348713×10¹¹
1.13650084×10¹¹
1.77036079×10¹⁷
4.94131623×10¹⁸
≥1
?
≥1
?
≥1
≥1
≥1
?
49
0
407638
0
1.27154532×10¹²
2.98634312×10¹¹
5.88148701×10¹⁷
1.88859990×10¹⁹
≥1
?
≥1
?
≥1
≥1
≥1
?
50
0
704540
0
3.09132945×10¹²
7.80626524×10¹¹
1.95402372×10¹⁸
7.21077467×10¹⁹
≥1
?
≥1
?
≥1
≥1
≥1
?
51
0
1190880
0
7.37082844×10¹²
2.04675006×10¹²
6.48969999×10¹⁸
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
52
0
2059175
0
1.78633971×10¹³
5.36663526×10¹²
2.15633494×10¹⁹
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
53
0
3523630
0
4.27046408×10¹³
1.40446235×10¹³
7.16176435×10¹⁹
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
54
0
6096680
0
1.03267175×10¹⁴
3.68318845×10¹³
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
55
0
10518320
0
2.47337938×10¹⁴
9.64375766×10¹³
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
56
0
18238174
0
5.97145281×10¹⁴
2.52787923×10¹⁴
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
≥1
≥1
≥1
≥1
?
57
0
31621296
0
1.43219229×10¹⁵
6.62167985×10¹⁴
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
58
0
54993228
0
3.45375501×10¹⁵
1.73524469×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
59
0
95636062
0
8.29145180×10¹⁵
4.54583703×10¹⁵
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
60
0
166755309
0
1.99790376×10¹⁶
1.19122789×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
61
0
290640282
0
4.79952852×10¹⁶
3.12087022×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
62
0
507729487
0
1.15587064×10¹⁷
8.17752765×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
63
0
886581304
0
2.77794728×10¹⁷
2.14258954×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
64
0
1.55073420×10¹⁰
0
6.68773162×10¹⁷
5.61379321×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
65
0
2.71194229×10¹⁰
0
1.60776010×10¹⁸
1.47091566×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
66
0
4.74765207×10¹⁰
0
3.86964590×10¹⁸
3.85397060×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
67
0
8.31219283×10¹⁰
0
9.30465308×10¹⁸
1.00978604×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
68
0
1.45617063×10¹¹
0
2.23912589×10¹⁹
2.64581599×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
69
0
2.55148760×10¹¹
0
5.38476804×10¹⁹
6.93226760×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
?
≥1
≥1
≥1
?
70
0
4.47232964×10¹¹
0
1.29567420×10²⁰
1.81637688×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
?
≥1
≥1
≥1
≥1
≥1
?
N>0
x
all
x
all
all
all
all
all
?
?
?
?
?
?

See Also

O tetromino and L pentominoO tetromino and P pentomino