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 C heptomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (10x11):

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 \ h1-789101112N>0
1-70
8000
900000
100000000
11000001100
1200000000000
1300000000011?
14000000011911922?
150000036360077?
160000044992626?
17000000000237237?
18000001187338733588588?
1902200136713670068356835?
20044121232432410861086C1791817918?
210660022005148351483?
22088004242C526500526500124372124372?
230505000530785307800972470972470?
24012412458858816484164847773477734C30315183031518?
250238238001371370085064578506457?
2604004000016191619C2876441628764416C2148547821485478C?
270115011500020157102015710C00108696079108696079C?
28028642864213322133272153672153646172714617271C370936019370936019C?
290616661660064786478C5425421.11316427×10¹⁰1113164275C?
3001188811888006321163211C1.48402690×10¹⁰1484026907C3.02702436×10¹⁰3027024363C?
3102708627086007498356474983564C5365361.17596026×10¹¹11759602647C?
32062872628726931346931342947614529476145C250577171250577171C4.05907082×10¹¹40590708286C?
33013890213890200272511272511C63952639521.27787093×10¹²127787093404C?
3402868262868260024257942425794C7.37697093×10¹¹73769709342C3.69957005×10¹²369957005137C?
350616588616588002.74707786×10¹⁰2747077861C89960899601.26454258×10¹³1264542586020C?
3601359046135904621205242212052421.15554128×10¹⁰1155541288C1.29013455×10¹¹12901345562C4.26316755×10¹³4263167555810C?
37029728302972830001087340610873406C480004848000481.36916176×10¹⁴13691617666881C?
38062986806298680C009119923891199238C3.57263575×10¹³3572635756666C4.13495679×10¹⁴41349567931567C?
3901338971613389716C009.94553264×10¹¹99455326459C89387528938752C1.33886728×10¹⁵133886728468566C?
4002878570428785704C624150656624150656C4.40405415×10¹¹44040541545C6.41699855×10¹²641699855716C4.39268994×10¹⁵439268994693146C?
4106204084262040842C00419778542419778542C296607668296607668C1.41387498×10¹⁶1413874981071510C?
420132096258132096258C003.37386361×10¹⁰3373863610C1.69713478×10¹⁵169713478177509C4.37452557×10¹⁶4374525576253520C?
430280209316280209316C003.56627084×10¹³3566270845268C691797604691797604C1.38772357×10¹⁷13877235741530462C?
440596047430596047430C1.78860028×10¹¹17886002820C1.64419768×10¹³1644197686039C3.11461289×10¹⁴31146128939338C4.46334394×10¹⁷44633439433302918C?
4501.27098628×10¹⁰1270986286C001.58261375×10¹¹15826137504C1.65265303×10¹¹16526530370C1.42903230×10¹⁸142903230973477091C?
4602.69957159×10¹⁰2699571592C001.23262811×10¹²123262811184C7.94306046×10¹⁶7943060468388050C4.47284172×10¹⁸447284172620139892C?
4705.71565778×10¹⁰5715657780C001.26864976×10¹⁵126864976386681C4.62601741×10¹¹46260174156C1.40896560×10¹⁹1408965607025300203C?
4801.20974042×10¹¹12097404224C5.02593816×10¹²502593816546C6.04235715×10¹⁴60423571561194C1.48436651×10¹⁶1484366519458238C4.47675784×10¹⁹4476757844897179264C?
4902.56272526×10¹¹25627252652C005.86060229×10¹²586060229118C8.65513091×10¹²865513091878C1.42361117×10²⁰14236111794979890080C?
5005.42226235×10¹¹54222623566C004.45825500×10¹³4458255003107C3.67395655×10¹⁸367395655594806821C≥1.84467440×10²⁰≥18446744073709551615C?
5101.14516035×10¹²114516035746C004.48284873×10¹⁶4482848736421675C2.81361825×10¹³2813618257856C≥1.84467440×10²⁰≥18446744073709551615C?
5202.41617587×10¹²241617587260C1.39120677×10¹⁴13912067734430C2.19309169×10¹⁶2193091699556354C6.97463251×10¹⁷69746325106440920C≥1.84467440×10²⁰≥18446744073709551615C?
5305.09748844×10¹²509748844968C002.14012853×10¹⁴21401285397859C4.35315000×10¹⁴43531500015002C≥1.84467440×10²⁰≥18446744073709551615C?
5401.07484149×10¹³1074841494400C001.59913929×10¹⁵159913929259138C1.68310896×10²⁰16831089638161705054C≥1.84467440×10²⁰≥18446744073709551615C?
5502.26412174×10¹³2264121746800C001.57498552×10¹⁸157498552640145984C1.60235939×10¹⁵160235939153056C≥1.84467440×10²⁰≥18446744073709551615C?
5604.76519234×10¹³4765192346916C3.80533916×10¹⁵380533916353332C7.88020320×10¹⁷78802032007174093C3.24028526×10¹⁹3240285266278624273C≥1.84467440×10²⁰≥18446744073709551615C?
5701.00247248×10¹⁴10024724846728C007.72828285×10¹⁵772828285763793C2.12848515×10¹⁶2128485153384212C≥1.84467440×10²⁰≥18446744073709551615C?
5802.10801524×10¹⁴21080152441958C005.69601258×10¹⁶5696012586074045C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5904.43002628×10¹⁴44300262825402C005.50614644×10¹⁹5506146449393396648C8.69844734×10¹⁶8698447344613438C≥1.84467440×10²⁰≥18446744073709551615C?
6009.30373168×10¹⁴93037316863768C1.03084332×10¹⁷10308433242182834C2.80808482×10¹⁹2808084826748912218C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6101.95297423×10¹⁵195297423680666C002.76539479×10¹⁷27653947912294813C1.01932323×10¹⁸101932323555343832C≥1.84467440×10²⁰≥18446744073709551615C?
6204.09783238×10¹⁵409783238728380C002.01681453×10¹⁸201681453409369309C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6308.59433778×10¹⁵859433778087448C00≥1.84467440×10²⁰≥18446744073709551615C4.55379481×10¹⁸455379481881973738C≥1.84467440×10²⁰≥18446744073709551615C?
6401.80159658×10¹⁶1801596589130178C2.77019122×10¹⁸277019122402978762C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6503.77495729×10¹⁶3774957296765012C009.82032558×10¹⁸982032558910821796C4.80434645×10¹⁹4804346457757857210C≥1.84467440×10²⁰≥18446744073709551615C?
6607.90674781×10¹⁶7906747817556712C007.10437906×10¹⁹7104379066683437334C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6701.65545707×10¹⁷16554570771261530C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6803.46471767×10¹⁷34647176724368466C7.39425205×10¹⁹7394252059255711136C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6907.24861339×10¹⁷72486133959703402C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7001.51597263×10¹⁸151597263740469010C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7103.16944976×10¹⁸316944976274077370C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7206.62420589×10¹⁸662420589636649762C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7301.38402801×10¹⁹1384028019169576880C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7402.89083773×10¹⁹2890837736613784798C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7506.03637440×10¹⁹6036374403514915372C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
7601.26010150×10²⁰12601015018041067976C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
770≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
780≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
790≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
800≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
N>0x?????

See Also

I tetromino and X2 hexominoI tetromino and U heptomino