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 (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 \ h1-7891011121314N>0
1-70
8000
90000
10000000
1100000000
120000000000
13000000000000
1400000000000022P
1500000000000000?
160000000000001616P?
170000000000002020P?
180000000044P00472472P?
190000000022P00≥260≥260P?
20011P033P00199199P5252P≥1≥1?
21000000001818P00≥1≥1P?
22033P01717P0012351235P148148P≥1≥1P?
23000022P00552552P3232P≥1≥1P?
24077P09393P0093649364P43624362P≥1≥1P?
25022P02626P001343013430P29642964P≥1≥1P?
2601414P0387387P007084370843P6555465554P≥1≥1P?
27088P0238238P00195640195640P132008132008P≥1≥1P?
2802626P019181918P296296P657452657452P10841461084146P≥1≥1C?
2902424P022442244P0023190402319040P33514763351476P≥1≥1P?
3005858P091609160P592592P70489697048969P1528200815282008P≥1≥1C?
3106262P01478214782P336336P2523003025230030P5840487658404876P≥1≥1C?
320133133P04760547605P23362336P7936141879361418P224783002224783002P≥1≥1C?
330146146P09229092290P72327232P270228548270228548P898749716898749716P≥1≥1C?
340312312P0265934265934P1612016120P891498126891498126P3.41362636×10¹⁰3413626368P≥1≥1C?
350354354P0549252549252P4004840048P2.93306176×10¹⁰2933061766P1.32488768×10¹¹13248876896P≥1≥1C?
360741741P015072201507220P112360112360P9.90062310×10¹⁰9900623105C5.10733051×10¹¹51073305184P≥1≥1C?
370910910P032164623216462P287152287152P3.22868616×10¹¹32286861612C1.93201381×10¹²193201381356P≥1≥1C?
38017921792P086087768608776P721896721896P1.09016063×10¹²109016063078C7.52582937×10¹²752582937048P≥1≥1C?
39024462446P01887343418873434P20041122004112P3.57648780×10¹²357648780472C2.82530320×10¹³2825303204560P≥1≥1C?
40044304430C04916483749164837C50056565005656P1.19759181×10¹³1197591812397C1.09903556×10¹⁴10990355637578C≥1≥1C?
41066586658P0110612984110612984P1334020813340208P3.96200967×10¹³3962009677584C4.14062536×10¹⁴41406253682728P≥1≥1C?
4201142011420C0281222202281222202C3602475236024752P1.31766376×10¹⁴13176637639448C1.59833753×10¹⁵159833753687546C≥1≥1C?
4301829618296P0646881282646881282C9073342490733424P4.37966013×10¹⁴43796601317996C6.06746530×10¹⁵606746530111236C≥1≥1C?
4403086030860C01.61332684×10¹⁰1613326841C244674488244674488P1.45285061×10¹⁵145285061145264C2.32488813×10¹⁶2324888130464420C≥1≥1C?
4505051050510C03.77000280×10¹⁰3770002804C627017392627017392P4.83346489×10¹⁵483346489409066C8.87330134×10¹⁶8873301342064020C≥1≥1C?
4608588185881C09.28309425×10¹⁰9283094253C1.66355302×10¹⁰1663553024P1.60364195×10¹⁶1603641952772070C3.38721905×10¹⁷33872190511580924C???
470141892141892C02.19140294×10¹¹21914029440C4.34951678×10¹⁰4349516784P5.33150442×10¹⁶5331504426732180C1.29509433×10¹⁸129509433827197816C???
480244269244269C05.35348713×10¹¹53534871336C1.13650084×10¹¹11365008488P1.77036079×10¹⁷17703607953998544C4.94131623×10¹⁸494131623258554454C???
490407638407638C01.27154532×10¹²127154532916C2.98634312×10¹¹29863431232P5.88148701×10¹⁷58814870101548366C1.88859990×10¹⁹1888599905996715356C???
500704540704540C03.09132945×10¹²309132945457C7.80626524×10¹¹78062652480P1.95402372×10¹⁸195402372403743032C7.21077467×10¹⁹7210774676690789616C???
51011908801190880C07.37082844×10¹²737082844190C2.04675006×10¹²204675006064P6.48969999×10¹⁸648969999001772746C≥1.84467440×10²⁰≥18446744073709551615C???
52020591752059175C01.78633971×10¹³1786339711194C5.36663526×10¹²536663526248P2.15633494×10¹⁹2156334946187470846C≥1.84467440×10²⁰≥18446744073709551615C???
53035236303523630C04.27046408×10¹³4270464084396C1.40446235×10¹³1404462353200P7.16176435×10¹⁹7161764355886744594C≥1.84467440×10²⁰≥18446744073709551615C???
54060966806096680C01.03267175×10¹⁴10326717564619C3.68318845×10¹³3683188455968P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
5501051832010518320C02.47337938×10¹⁴24733793825066C9.64375766×10¹³9643757664816P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
5601823817418238174C05.97145281×10¹⁴59714528119594C2.52787923×10¹⁴25278792394752C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
5703162129631621296C01.43219229×10¹⁵143219229690882C6.62167985×10¹⁴66216798519824P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
5805499322854993228C03.45375501×10¹⁵345375501369507C1.73524469×10¹⁵173524469107504C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
5909563606295636062C08.29145180×10¹⁵829145180432444C4.54583703×10¹⁵454583703657488C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
600166755309166755309C01.99790376×10¹⁶1997903769663129C1.19122789×10¹⁶1191227890268136C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
610290640282290640282C04.79952852×10¹⁶4799528520729786C3.12087022×10¹⁶3120870228976720C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
620507729487507729487C01.15587064×10¹⁷11558706478889065C8.17752765×10¹⁶8177527658209096C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
630886581304886581304C02.77794728×10¹⁷27779472860654762C2.14258954×10¹⁷21425895406201072C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6401.55073420×10¹⁰1550734200C06.68773162×10¹⁷66877316227841713C5.61379321×10¹⁷56137932193214096C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6502.71194229×10¹⁰2711942290C01.60776010×10¹⁸160776010294765596C1.47091566×10¹⁸147091566761699376C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6604.74765207×10¹⁰4747652077C03.86964590×10¹⁸386964590772649116C3.85397060×10¹⁸385397060473289016C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6708.31219283×10¹⁰8312192830C09.30465308×10¹⁸930465308576259684C1.00978604×10¹⁹1009786044890015760C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6801.45617063×10¹¹14561706307C02.23912589×10¹⁹2239125896215995868C2.64581599×10¹⁹2645815993423070688C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
6902.55148760×10¹¹25514876078C05.38476804×10¹⁹5384768042595925580C6.93226760×10¹⁹6932267607337742992C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
7004.47232964×10¹¹44723296450C01.29567420×10²⁰12956742061375778399C1.81637688×10²⁰18163768823269956800C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C???
N>0xallxallallallallall

See Also

O tetromino and L pentominoO tetromino and P pentomino