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 (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 \ h12345678910N>0
10
2000
300088P
40000000
500000003232P
60007272C2020P480480P≥1000≥1000C
700044P8888P26882688P≥1000≥1000C≥1000≥1000C
800000312312P1242012420P≥1000≥1000C≥1000≥1000C≥1000≥1000C
9088P656656C11601160C5567655676C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
100008080C33363336P215490215490C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
110008080P1083210832P928600928600C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1200059845984C3032630326C38719343871934C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1302424P11361136C9092490924C1732959217329592C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1402424P11601160C255354255354C7619573276195732C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
150005464054640C756490756490C341915268341915268C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
160001408014080C21597862159786C1.51718228×10¹⁰1517182286C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1706464P1476814768C64039426403942C6.75769643×10¹⁰6757696436C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1809696C499424499424C1851911818519118C2.99127256×10¹¹29912725644C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
1906464P163056163056C5467793654677936C1.32100628×10¹²132100628636C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
20000175232175232C158728364158728364C5.81806789×10¹²581806789002C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
210160160P45696164569616C465484504465484504C2.55917511×10¹³2559175115800C??????????all
220320320C18040161804016C1.35059833×10¹⁰1350598334C1.12652323×10¹⁴11265232372032C??????????all
230320320C19896801989680C3.94051790×10¹⁰3940517906C4.96376345×10¹⁴49637634520612C??????????all
240160160P4185548841855488C1.14309933×10¹¹11430993392C2.19071441×10¹⁵219071441922168C??????????all
250384384P1937446419374464C3.32778116×10¹¹33277811636C9.67500107×10¹⁵967500107165960C??????????all
260960960C2191987221919872C9.66174860×10¹¹96617486032C4.27399256×10¹⁶4273992568291136C??????????all
27012801280C383798144383798144C2.81151822×10¹²281151822266C1.88729425×10¹⁷18872942504829188C??????????all
280960960C203668064203668064C8.17091269×10¹²817091269260C8.33017651×10¹⁷83301765174112598C??????????all
29012801280P236223232236223232C2.37763018×10¹³2377630188976C3.67534578×10¹⁸367534578969990332C??????????all
30026882688C3.52319225×10¹⁰3523192256C6.91349983×10¹³6913499836890C1.62137349×10¹⁹1621373490869900556C??????????all
31044804480C2.10679801×10¹⁰2106798016C2.01140730×10¹⁴20114073055814C7.15291249×10¹⁹7152912497551159732C??????????all
32044804480C2.50326400×10¹⁰2503264000C5.84919268×10¹⁴58491926859908C≥1.84467440×10²⁰≥18446744073709551615C??????????all
33047364736C3.23789538×10¹¹32378953856C1.70135616×10¹⁵170135616983996C≥1.84467440×10²⁰≥18446744073709551615C??????????all
34080648064C2.15221812×10¹¹21522181248C4.94737343×10¹⁵494737343383602C≥1.84467440×10²⁰≥18446744073709551615C??????????all
3501433614336C2.61778192×10¹¹26177819264C1.43882054×10¹⁶1438820544758250C≥1.84467440×10²⁰≥18446744073709551615C??????????all
3601792017920C2.97912993×10¹²297912993600C4.18391002×10¹⁶4183910026425112C≥1.84467440×10²⁰≥18446744073709551615C??????????all
3701894418944C2.17678177×10¹²217678177152C1.21672729×10¹⁷12167272973633996C≥1.84467440×10²⁰≥18446744073709551615C??????????all
3802560025600C2.70832285×10¹²270832285696C3.53820116×10¹⁷35382011661753652C≥1.84467440×10²⁰≥18446744073709551615C??????????all
3904505645056C2.74423955×10¹³2744239552064C1.02895082×10¹⁸102895082295936798C≥1.84467440×10²⁰≥18446744073709551615C??????????all
4006451264512C2.18382230×10¹³2183822304768C2.99224835×10¹⁸299224835669487682C≥1.84467440×10²⁰≥18446744073709551615C??????????all
N>0xallallallallallallallallall

See Also

L tetromino and N pentominoL tetromino and R pentomino