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.


U pentomino and C hexomino

Prime rectangles: ≥ 47.

Smallest rectangle tilings

Smallest rectangle (12x14):

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 \ h1-1112131415-1617181920212223N>0
1-110
12000
1300000
14011P0000
15-1600000000
170000000000
18011P000000000
1900000000000000
20000000000022P0000
21000000000000000000
22011P00000000000000088P
23044P000000000??????????
240000022C00022C??????≥1≥1C≥1≥1C?
25000000000000???????????
26011P000000044P???????????
2701616P000000000???????????
28011C00000001212P???????????
29022P000000000???????????
30011P00000001818P???????????
3103636P000000000???????????
3201111C0022P0001111C???????????
33044P00000???????????????
34011P00000??110110P??????≥1≥1C???
3506464P00000???????????????
360106106C0044C0??≥1≥1C??≥1≥1C??≥1≥1C≥1≥1C?
3701414C00000???????????????
3802121P00000??≥1≥1C???????????
390100100P00000???????????????
400451451C00000??≥1≥1C???????????
4106464C00000???????????????
4209494C00000??≥1≥1C???????????
430148148C00000???????????????
44013161316C0088C0??≥1≥1C??????≥1≥1C???
450562562C00000???????????????
460288288C00000??≥1≥1C??????≥1≥1C???
470324324C00000???????????????
48030613061C88P88C0??≥1≥1C??????≥1≥1C≥1≥1C?
49035603560C00000???????????????
500920920C00000???????????????
51012561256C00000???????????????
52061986198C0044P0???????????????
5301538615386C00000???????????????
54042064206C00000???????????????
55047004700C00000???????????????
5601193811938C1616P2424C0???????????????
5705053450534C00000???????????????
5802527325273C44P000???????????????
5901587215872C00000???????????????
6002653726537C3232P1616C0???????????????
610137214137214C00000???????????????
620135539135539C00000???????????????
6305558855588C00000???????????????
6407651776517C3232P2424C0???????????????
650327542327542C00000???????????????
660580298580298C2020P000???????????????
670236052236052C00000???????????????
680253935253935C152152P6464C0???????????????
690738178738178C00000???????????????
70020316992031699C88P000???????????????
71011713001171300C00000???????????????
720877318877318C140140P4242C0???????????????
73017434401743440C00000???????????????
74060793506079350C6868P000???????????????
75056213285621328C00000???????????????
76031828683182868C456456P9696C0???????????????
77047182524718252C00000???????????????
7801625077816250778C104104P000???????????????
7902357322623573226C00000???????????????
8001284120212841202C760760P160160C0???????????????
8101470581814705818C00000???????????????
8204094443740944437C224224P88P0???????????????
8308538112885381128C00000???????????????
8405685290456852904C13901390P140140C0???????????????
8505010012650100126C00000???????????????
860104167143104167143C588588P000???????????????
870272548976272548976C00000???????????????
880250904667250904667C32343234P340340C0???????????????
890181348338181348338C00000???????????????
900286457116286457116C904904P88P0???????????????
910790950544790950544C00000???????????????
9201.02331150×10¹⁰1023311500C50165016P418418C0???????????????
930703455004703455004C00000???????????????
940877291954877291954C25202520P6060C0???????????????
9502.17295971×10¹⁰2172959712C00000???????????????
9603.76338141×10¹⁰3763381411C1186411864C496496C0???????????????
9702.89123858×10¹⁰2891238584C00000???????????????
9802.93670831×10¹⁰2936708312C44124412P1616P0???????????????
9905.94263198×10¹⁰5942631982C00000???????????????
10001.25496555×10¹¹12549655573C2050820508P10641064C0???????????????
N>0xall??x???????

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
U pentomino000000000
C hexomino00000000?

Smallest common multiples

Smallest known common multiple (area 60):

Common multiples' solutions count (excluding symmetric)

area3060
solutions?≥1

Attributions

  1. Smallest known common multiple is found by Giovanni Resta (http://www.iread.it/Poly/P65.html)

See Also

U pentomino and B hexominoU pentomino and D hexomino