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 tetromino and U heptomino

Prime rectangles: 38.

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
1
0
0
2
7
0
0
0
0
8
0
8
0
0
0
0
0
2
8
9
0
0
0
0
3
0
14
0
10
0
3
0
2
27
136
32
264
1956
11
0
0
0
0
66
4
100
136
6201
856
12
0
1
2
3
9
150
618
1392
4924
27723
≥1
13
0
0
4
0
54
8
1432
236
21808
20956
≥1
≥1
14
0
6
6
22
264
1826
2956
12650
110338
522714
≥1
≥1
≥1
15
0
0
8
0
524
124
6216
8422
301429
188048
≥1
≥1
≥1
≥1
16
0
5
20
39
185
3646
23308
73093
422519
3649585
≥1
≥1
≥1
≥1
≥1
17
0
0
36
0
648
300
58314
17226
1454193
2584518
≥1
≥1
≥1
≥1
≥1
≥1
18
0
11
56
168
2342
23340
126160
518143
5959078
44616448
≥1
≥1
≥1
≥1
≥1
≥1
≥1
19
0
0
80
0
4147
2456
260460
361282
15343383
27396070
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
20
0
15
138
349
2446
64140
728570
3194867
29155677
374194177
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
21
0
0
224
0
6701
7752
1802732
928348
88694611
302441340
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
22
0
22
344
1146
19904
301098
4033110
19843868
318477323
3.86505092×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
23
0
0
504
0
33045
41900
8547626
14146594
805906648
3.26252242×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
24
0
36
784
2618
26827
979183
20963348
127022032
1.80996414×10¹⁰
3.49043936×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
1204
2
64066
157688
50143304
44574968
5.17914207×10¹⁰
3.35999769×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
26
0
49
1812
7426
165549
3968046
113473994
732793296
1.70319771×10¹¹
3.37293416×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
27
0
0
2664
0
265289
687508
246014400
538833848
4.31978231×10¹¹
3.53638097×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
28
0
79
4000
17901
267395
13947455
571283648
4.76750044×10¹⁰
1.06518296×10¹²
3.13740305×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
0
0
5988
32
584438
2781120
1.32914851×10¹⁰
1.98687555×10¹⁰
2.95593216×10¹²
3.56044058×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
30
0
113
8888
46608
1361765
53101928
3.00802158×10¹⁰
2.64787002×10¹¹
9.15830331×10¹²
2.95617536×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
0
0
13032
4
2145944
11129808
6.60835036×10¹⁰
2.02399089×10¹¹
2.34686210×10¹³
3.65437133×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
32
0
171
19266
115945
2518732
192238649
1.49960592×10¹¹
1.72685919×10¹²
6.09650763×10¹³
2.78122033×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
0
0
28468
308
5172820
45375420
3.42759870×10¹¹
8.39009530×10¹¹
1.66669671×10¹⁴
3.64183460×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
34
0
257
41894
286028
11142934
715432214
7.73099886×10¹¹
9.43343501×10¹²
4.95849889×10¹⁴
2.60061731×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
35
0
0
61224
80
17480456
177143776
1.70986453×10¹²
7.53171387×10¹²
1.28658194×10¹⁵
3.67115783×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
36
0
376
89750
725012
22872412
2.61254634×10¹⁰
3.83952222×10¹²
6.11744258×10¹³
3.43841927×10¹⁵
2.45608153×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
0
0
131568
2394
44859564
710637660
8.68053429×10¹²
3.40559978×10¹³
9.33787219×10¹⁵
3.63336897×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
38
0
573
192470
1726192
91020148
9.65259504×10¹⁰
1.95069282×10¹³
3.32766518×10¹⁴
2.70261752×10¹⁶
2.29569467×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
39
0
0
280408
964
143231960
2.76175075×10¹⁰
4.32821786×10¹³
2.78363299×10¹⁴
7.09594115×10¹⁶
3.61803502×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
40
0
838
408876
4424064
202562752
3.53186488×10¹¹
9.66857378×10¹³
2.13693818×10¹⁵
1.92472118×10¹⁷
2.17030479×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
0
0
596156
16762
383609935
1.08814157×10¹¹
2.17097381×10¹⁴
1.34292787×10¹⁵
5.21516563×10¹⁷
3.56096153×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
42
0
1266
868214
10284006
743725989
1.30172616×10¹²
4.86290486×10¹⁴
1.16535897×10¹⁶
1.48162598×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
0
0
1261312
9182
1.17898747×10¹⁰
4.22251725×10¹¹
1.08050110×10¹⁵
1.02328027×10¹⁶
3.92948548×10¹⁸
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
44
0
1873
1832314
26519897
1.76237895×10¹⁰
4.76655464×10¹²
2.40713422×10¹⁵
7.39909688×10¹⁶
1.07358445×10¹⁹
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
0
0
2661236
110896
3.24879644×10¹⁰
1.64223086×10¹²
5.38142331×10¹⁵
5.18301170×10¹⁶
2.90876128×10¹⁹
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
46
0
2798
3862360
60646436
6.08572103×10¹⁰
1.75449489×10¹³
1.20226720×10¹⁶
4.05917395×10¹⁷
8.16127979×10¹⁹
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
47
0
0
5597088
76336
9.73682269×10¹⁰
6.35376132×10¹²
2.67254355×10¹⁶
3.74457391×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
48
0
4174
8108114
156853530
1.51380430×10¹¹
6.42961880×10¹³
5.94511885×10¹⁶
2.54792714×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
0
0
11742256
709004
2.73316760×10¹¹
2.45115012×10¹³
1.32541283×10¹⁷
1.96799734×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
50
0
6204
16996632
354716802
4.98943290×10¹¹
2.36436810×10¹⁴
2.95512113×10¹⁷
1.40824096×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
0
0
24578272
581626
8.05956803×10¹¹
9.44364902×10¹³
6.56872049×10¹⁷
1.36479937×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
52
0
9273
35527186
918113319
1.28817389×10¹²
8.67175102×10¹⁴
1.45998410×10¹⁸
8.74517554×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
0
0
51337716
4431040
2.28895345×10¹²
3.62450541×10¹⁴
3.24917818×10¹⁸
7.37814813×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
54
0
13785
74155614
2.06082282×10¹⁰
4.09899816×10¹²
3.18680205×10¹⁵
7.23340029×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
55
0
0
107045384
4177054
6.68109004×10¹²
1.39032276×10¹⁵
1.60743793×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
56
0
20576
154462936
5.32987004×10¹⁰
1.08867815×10¹³
1.16960296×10¹⁶
3.57084478×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
0
0
222819172
27246084
1.91105198×10¹³
5.31654271×10¹⁵
7.93797974×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
58
0
30640
321325276
1.19063865×10¹¹
3.37397673×10¹³
4.29678690×10¹⁶
1.76524245×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
59
0
0
463166976
28769402
5.54339778×10¹³
2.03141059×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
60
0
45664
667398784
3.07363231×10¹¹
9.15463715×10¹³
1.57772573×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
0
0
961428524
165502844
1.59226426×10¹⁴
7.74474965×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
62
0
68072
1.38463427×10¹⁰
6.84683091×10¹¹
2.78193540×10¹⁴
5.79564588×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
63
0
0
1.99345220×10¹⁰
192145306
4.60181247×10¹⁴
2.94954662×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
64
0
101392
2.86916232×10¹⁰
1.76292006×10¹²
7.66986450×10¹⁴
2.12876265×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
0
0
4.12859375×10¹⁰
995868600
1.32485722×10¹⁵
1.12155748×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
66
0
151169
5.93954104×10¹⁰
3.92175232×10¹²
2.29709476×10¹⁵
7.82038856×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
67
0
0
8.54260543×10¹⁰
1.25352360×10¹⁰
3.82117011×10¹⁵
4.25984622×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
68
0
225192
1.22836380×10¹¹
1.00663300×10¹³
6.40877102×10¹⁵
2.87312120×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
0
0
1.76593753×10¹¹
5.94765457×10¹⁰
1.10139028×10¹⁶
1.61600030×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
70
0
335659
2.53829152×10¹¹
2.23873639×10¹³
1.89900295×10¹⁶
1.05564525×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
0
0
3.64768808×10¹¹
8.02795365×10¹⁰
3.17330087×10¹⁶
6.12385216×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
72
0
500161
5.24095349×10¹¹
5.72655937×10¹³
5.34471346×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
0
0
7.52882823×10¹¹
3.53075095×10¹¹
9.15104391×10¹⁶
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
74
0
745342
1.08136987×10¹²
1.27427734×10¹⁴
1.57139758×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
75
0
0
1.55291596×10¹²
5.06510559×10¹¹
2.63533144×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
76
0
1110789
2.22972906×10¹²
3.24759746×10¹⁴
4.45116834×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
77
0
0
3.20104649×10¹²
2.08566059×10¹²
7.60062507×10¹⁷
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
78
0
1655187
4.59485571×10¹²
7.23492201×10¹⁴
1.30128899×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
79
0
0
6.59464191×10¹²
3.15661411×10¹²
2.18851109×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
80
0
2466759
9.46351320×10¹²
1.83691507×10¹⁵
3.70337271×10¹⁸
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
2k
all
all
all
all
all
all
all
all
all
?
?
?
?
?
?
?
?

See Also

I tetromino and C heptominoL tetromino and O tetromino