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 pentomino and Y2 hexomino

Prime rectangles: ≥ 43.

Smallest rectangle tilings

Smallest rectangle and smallest square (22x22):

Rectangle tilings' solutions count (including symmetric)

Blue number (P) - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number (W) - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Red number (C) - 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 \ h1-13141516171819202122N>0
1-130
14000
150000
16000000
1700000000
180000000000
19000000000000
2000000000000000
210000000000000000
22000000000000000022P
23000000000000000000?
24000000000000000000?
25000000000000000000?
26000000000000000000?
27000000000000000000?
28000000000000000022P?
29000000000000000000?
30000000000000000000?
31000000?????????????
32000000?????????????
33000000?????????????
34000000?????????????
35000000?????????????
36000000?????????????
37000000?????????????
38000000?????????????
39000000?????????????
40000000?????????????
41000000?????????????
42022P000?????????????
43000000?????????????
44000000?????????????
45000000?????????????
46000000?????????????
47000000?????????????
48044P000?????????????
49000000?????????????
50000000?????????????
51000000?????????????
52000000?????????????
53000000?????????????
54066P000?????????????
55000000?????????????
56022P000?????????????
57000000?????????????
58000000?????????????
59000000?????????????
6001414P000?????????????
61000000?????????????
6201212P000?????????????
63000000?????????????
640000???????????????
65022P0???????????????
6603434P0???????????????
670000???????????????
6804242P0???????????????
69044P0???????????????
700000???????????????
71044P0???????????????
7208080P0???????????????
730000???????????????
740116116P0???????????????
7502626P0???????????????
76044P0???????????????
7702626P0???????????????
780196196P0???????????????
7901616P0???????????????
800332332P0???????????????
810148148P0???????????????
8202828P0???????????????
830178178P0???????????????
840526526C0???????????????
850124124P0???????????????
860844844P0???????????????
870596596P0???????????????
880224224P0???????????????
890900900P0???????????????
90016041604C0???????????????
910588588P0???????????????
92024722472P0???????????????
93022382238P0???????????????
94011781178P0???????????????
95036743674P0???????????????
96051725172C0???????????????
97023962396P0???????????????
98087068706C0???????????????
99081388138P0???????????????
100049204920P0???????????????
10101329813298P0???????????????
10201637016370C0???????????????
103092409240P0???????????????
10403069430694C0???????????????
10502796427964P0???????????????
10601867018670P0???????????????
10704631846318C0???????????????
10805232452324C0???????????????
10903551035510P0???????????????
1100105816105816C0???????????????
11109284692846C0???????????????
11206782867828C0???????????????
1130154166154166C0???????????????
1140169102169102C0???????????????
1150137014137014P0???????????????
1160360354360354C0???????????????
1170303804303804C0???????????????
1180245582245582C0???????????????
1190510748510748C0???????????????
1200556130556130C0???????????????
1210522160522160C0???????????????
122012166601216660C0???????????????
1230997712997712C0???????????????
1240885350885350C0???????????????
125017158481715848C0???????????????
126018638641863864C0???????????????
127019470421947042C0???????????????
128040993484099348C0???????????????
129033366243336624C0???????????????
130032164403216440C0???????????????
131058413085841308C0???????????????
132063593766359376C0???????????????
133071346487134648C0???????????????
13401384956213849562C0???????????????
13501139335211393352C0???????????????
13601176682411766824C0???????????????
13702018768420187684C0???????????????
13802206024022060240C0???????????????
13902580645425806454C0???????????????
14004694219046942190C0???????????????
14103957517239575172C0???????????????
14204302818443028184C0???????????????
14307051820270518202C0???????????????
14407728860677288606C0???????????????
14509267069092670690C0???????????????
1460159866670159866670C0???????????????
1470139239438139239438C0???????????????
1480157167462157167462C0???????????????
1490247666488247666488C0???????????????
1500272162008272162008C0???????????????
1510331491680331491680C0???????????????
1520546455998546455998C0???????????????
1530493208686493208686C0???????????????
1540572593914572593914C0???????????????
1550871689958871689958C0???????????????
1560960901542960901542C0???????????????
15701.18393882×10¹⁰1183938828C0???????????????
15801.87238165×10¹⁰1872381658C0???????????????
15901.75190501×10¹⁰1751905012C0???????????????
16002.07797714×10¹⁰2077977142C0???????????????
16103.06841539×10¹⁰3068415394C0???????????????
16203.39491573×10¹⁰3394915738C0???????????????
16304.22431149×10¹⁰4224311496C0???????????????
16406.42792118×10¹⁰6427921186C0???????????????
16506.22844913×10¹⁰6228449130C0???????????????
16607.51069110×10¹⁰7510691102C0???????????????
16701.07925833×10¹¹10792583366C0???????????????
16801.19975117×10¹¹11997511740C0???????????????
16901.50529436×10¹¹15052943642C0???????????????
17002.21104461×10¹¹22110446166C0???????????????
17102.21437807×10¹¹22143780786C0???????????????
17202.70481493×10¹¹27048149330C0???????????????
17303.79334575×10¹¹37933457572C0???????????????
17404.24198171×10¹¹42419817132C0???????????????
17505.35657652×10¹¹53565765250C0???????????????
17607.62432107×10¹¹76243210742C0???????????????
17707.87182768×10¹¹78718276838C0???????????????
17809.70998903×10¹¹97099890354C0???????????????
17901.33287876×10¹²133287876050C0???????????????
18001.50077779×10¹²150077779696C0???????????????
18101.90348398×10¹²190348398058C0???????????????
18202.63693893×10¹²263693893210C0???????????????
18302.79836786×10¹²279836786152C0???????????????
18403.47663590×10¹²347663590576C0???????????????
18504.68452611×10¹²468452611198C0???????????????
18605.31383457×10¹²531383457954C0???????????????
18706.75601333×10¹²675601333846C0???????????????
18809.15025406×10¹²915025406318C0???????????????
18909.94845991×10¹²994845991700C0???????????????
19001.24209932×10¹³1242099321330C0???????????????
19101.64750382×10¹³1647503829970C0???????????????
19201.88299358×10¹³1882993583254C0???????????????
19302.39574368×10¹³2395743685028C0???????????????
19403.18587841×10¹³3185878415200C0???????????????
19503.53689311×10¹³3536893114750C0???????????????
19604.42966966×10¹³4429669660976C0???????????????
19705.79918874×10¹³5799188744766C0???????????????
19806.67705101×10¹³6677051016980C0???????????????
19908.49045012×10¹³8490450121806C0???????????????
20001.11274282×10¹⁴11127428222382C0???????????????
N>0xallx???????

See Also

T pentomino and Y1 hexominoU pentomino and V pentomino