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 U heptomino

Prime rectangles: 38.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

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 \ h1-234567891011N>0
1-20
300
400000
5000000
6011P000022C
700000088P00
800000000022P88P
900000033C001414P00
10033P0022P2727C136136P3232C264264C19561956C
110000006666P44P100100P136136P62016201C856856P
12011C22P33P99C150150C618618C13921392C49244924C2772327723Call
130044P005454C88P14321432C236236P2180821808C2095620956C?
14066P66P2222P264264C18261826C29562956C1265012650C110338110338C522714522714C?
150088P00524524C124124P62166216C84228422P301429301429C188048188048C?
16055C2020P3939P185185C36463646C2330823308C7309373093C422519422519C36495853649585C?
17003636P00648648C300300C5831458314C1722617226C14541931454193C25845182584518C?
1801111C5656P168168P23422342C2334023340C126160126160C518143518143C59590785959078C4461644844616448C?
19008080P0041474147C24562456C260460260460C361282361282C1534338315343383C2739607027396070C?
2001515C138138P349349C24462446C6414064140C728570728570C31948673194867C2915567729155677C374194177374194177C?
2100224224P0067016701C77527752C18027321802732C928348928348C8869461188694611C302441340302441340C?
2202222C344344P11461146C1990419904C301098301098C40331104033110C1984386819843868C318477323318477323C3.86505092×10¹⁰3865050924C?
2300504504P003304533045C4190041900C85476268547626C1414659414146594C805906648805906648C3.26252242×10¹⁰3262522424C?
2403636C784784C26182618C2682726827C979183979183C2096334820963348C127022032127022032C1.80996414×10¹⁰1809964144C3.49043936×10¹¹34904393682C?
250012041204C22P6406664066C157688157688C5014330450143304C4457496844574968C5.17914207×10¹⁰5179142078C3.35999769×10¹¹33599976916C?
2604949C18121812C74267426C165549165549C39680463968046C113473994113473994C732793296732793296C1.70319771×10¹¹17031977106C3.37293416×10¹²337293416302C?
270026642664C00265289265289C687508687508C246014400246014400C538833848538833848C4.31978231×10¹¹43197823159C3.53638097×10¹²353638097016C?
2807979C40004000C1790117901C267395267395C1394745513947455C571283648571283648C4.76750044×10¹⁰4767500442C1.06518296×10¹²106518296422C3.13740305×10¹³3137403055433C?
290059885988C3232P584438584438C27811202781120C1.32914851×10¹⁰1329148510C1.98687555×10¹⁰1986875550C2.95593216×10¹²295593216004C3.56044058×10¹³3560440586818C?
300113113C88888888C4660846608C13617651361765C5310192853101928C3.00802158×10¹⁰3008021584C2.64787002×10¹¹26478700218C9.15830331×10¹²915830331371C2.95617536×10¹⁴29561753610891C?
31001303213032C44P21459442145944C1112980811129808C6.60835036×10¹⁰6608350366C2.02399089×10¹¹20239908914C2.34686210×10¹³2346862100663C3.65437133×10¹⁴36543713368034C?
320171171C1926619266C115945115945C25187322518732C192238649192238649C1.49960592×10¹¹14996059250C1.72685919×10¹²172685919788C6.09650763×10¹³6096507631764C2.78122033×10¹⁵278122033419793C?
33002846828468C308308P51728205172820C4537542045375420C3.42759870×10¹¹34275987080C8.39009530×10¹¹83900953024C1.66669671×10¹⁴16666967177798C3.64183460×10¹⁵364183460810232C?
340257257C4189441894C286028286028C1114293411142934C715432214715432214C7.73099886×10¹¹77309988626C9.43343501×10¹²943343501392C4.95849889×10¹⁴49584988986378C2.60061731×10¹⁶2600617314724821C?
35006122461224C8080C1748045617480456C177143776177143776C1.70986453×10¹²170986453184C7.53171387×10¹²753171387868C1.28658194×10¹⁵128658194856322C3.67115783×10¹⁶3671157835212668C?
360376376C8975089750C725012725012C2287241222872412C2.61254634×10¹⁰2612546348C3.83952222×10¹²383952222675C6.11744258×10¹³6117442585394C3.43841927×10¹⁵343841927319472C2.45608153×10¹⁷24560815360559075C?
3700131568131568C23942394C4485956444859564C710637660710637660C8.68053429×10¹²868053429206C3.40559978×10¹³3405599783220C9.33787219×10¹⁵933787219351689C3.63336897×10¹⁷36333689774665232C?
380573573C192470192470C17261921726192C9102014891020148C9.65259504×10¹⁰9652595046C1.95069282×10¹³1950692821559C3.32766518×10¹⁴33276651843455C2.70261752×10¹⁶2702617524186277C2.29569467×10¹⁸229569467271818835C?
3900280408280408C964964C143231960143231960C2.76175075×10¹⁰2761750752C4.32821786×10¹³4328217863004C2.78363299×10¹⁴27836329952272C7.09594115×10¹⁶7095941153745638C3.61803502×10¹⁸361803502011204776C?
400838838C408876408876C44240644424064C202562752202562752C3.53186488×10¹¹35318648802C9.66857378×10¹³9668573782463C2.13693818×10¹⁵213693818808001C1.92472118×10¹⁷19247211824077055C2.17030479×10¹⁹2170304798768943474C?
4100596156596156C1676216762C383609935383609935C1.08814157×10¹¹10881415744C2.17097381×10¹⁴21709738128322C1.34292787×10¹⁵134292787684370C5.21516563×10¹⁷52151656314662438C3.56096153×10¹⁹3560961535272378742C?
42012661266C868214868214C1028400610284006C743725989743725989C1.30172616×10¹²130172616516C4.86290486×10¹⁴48629048617245C1.16535897×10¹⁶1165358979154836C1.48162598×10¹⁸148162598009217634C≥1.84467440×10²⁰≥18446744073709551615C?
430012613121261312C91829182C1.17898747×10¹⁰1178987475C4.22251725×10¹¹42225172596C1.08050110×10¹⁵108050110623362C1.02328027×10¹⁶1023280278502676C3.92948548×10¹⁸392948548254731558C≥1.84467440×10²⁰≥18446744073709551615C?
44018731873C18323141832314C2651989726519897C1.76237895×10¹⁰1762378955C4.76655464×10¹²476655464292C2.40713422×10¹⁵240713422576879C7.39909688×10¹⁶7399096887618908C1.07358445×10¹⁹1073584456834732863C≥1.84467440×10²⁰≥18446744073709551615C?
450026612362661236C110896110896C3.24879644×10¹⁰3248796447C1.64223086×10¹²164223086076C5.38142331×10¹⁵538142331718422C5.18301170×10¹⁶5183011701482302C2.90876128×10¹⁹2908761283623331371C≥1.84467440×10²⁰≥18446744073709551615C?
46027982798C38623603862360C6064643660646436C6.08572103×10¹⁰6085721032C1.75449489×10¹³1754494894010C1.20226720×10¹⁶1202267209638845C4.05917395×10¹⁷40591739548678870C8.16127979×10¹⁹8161279793703525589C≥1.84467440×10²⁰≥18446744073709551615C?
470055970885597088C7633676336C9.73682269×10¹⁰9736822698C6.35376132×10¹²635376132320C2.67254355×10¹⁶2672543559851790C3.74457391×10¹⁷37445739129339564C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
48041744174C81081148108114C156853530156853530C1.51380430×10¹¹15138043042C6.42961880×10¹³6429618807906C5.94511885×10¹⁶5945118851124452C2.54792714×10¹⁸254792714216407097C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
49001174225611742256C709004709004C2.73316760×10¹¹27331676061C2.45115012×10¹³2451150124492C1.32541283×10¹⁷13254128379895200C1.96799734×10¹⁸196799734896024480C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
50062046204C1699663216996632C354716802354716802C4.98943290×10¹¹49894329064C2.36436810×10¹⁴23643681070842C2.95512113×10¹⁷29551211307376550C1.40824096×10¹⁹1408240967626349654C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
51002457827224578272C581626581626C8.05956803×10¹¹80595680389C9.44364902×10¹³9443649026684C6.56872049×10¹⁷65687204972142600C1.36479937×10¹⁹1364799377095351214C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
52092739273C3552718635527186C918113319918113319C1.28817389×10¹²128817389727C8.67175102×10¹⁴86717510224311C1.45998410×10¹⁸145998410810717228C8.74517554×10¹⁹8745175548901231275C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
53005133771651337716C44310404431040C2.28895345×10¹²228895345092C3.62450541×10¹⁴36245054169536C3.24917818×10¹⁸324917818524853092C7.37814813×10¹⁹7378148131639057228C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5401378513785C7415561474155614C2.06082282×10¹⁰2060822820C4.09899816×10¹²409899816815C3.18680205×10¹⁵318680205060998C7.23340029×10¹⁸723340029538261441C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5500107045384107045384C41770544177054C6.68109004×10¹²668109004915C1.39032276×10¹⁵139032276782720C1.60743793×10¹⁹1607437934613796970C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5602057620576C154462936154462936C5.32987004×10¹⁰5329870048C1.08867815×10¹³1088678153057C1.16960296×10¹⁶1169602962289644C3.57084478×10¹⁹3570844785264663688C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5700222819172222819172C2724608427246084C1.91105198×10¹³1911051985659C5.31654271×10¹⁵531654271199628C7.93797974×10¹⁹7937979747828019278C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5803064030640C321325276321325276C1.19063865×10¹¹11906386576C3.37397673×10¹³3373976738968C4.29678690×10¹⁶4296786903864942C1.76524245×10²⁰17652424523268904003C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
5900463166976463166976C2876940228769402C5.54339778×10¹³5543397789059C2.03141059×10¹⁶2031410593947824C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6004566445664C667398784667398784C3.07363231×10¹¹30736323168C9.15463715×10¹³9154637152042C1.57772573×10¹⁷15777257317578317C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6100961428524961428524C165502844165502844C1.59226426×10¹⁴15922642632154C7.74474965×10¹⁶7744749650695996C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
6206807268072C1.38463427×10¹⁰1384634274C6.84683091×10¹¹68468309128C2.78193540×10¹⁴27819354023350C5.79564588×10¹⁷57956458870947190C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
63001.99345220×10¹⁰1993452208C192145306192145306C4.60181247×10¹⁴46018124786667C2.94954662×10¹⁷29495466233459812C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
640101392101392C2.86916232×10¹⁰2869162324C1.76292006×10¹²176292006690C7.66986450×10¹⁴76698645050256C2.12876265×10¹⁸212876265034999311C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
65004.12859375×10¹⁰4128593752C995868600995868600C1.32485722×10¹⁵132485722045856C1.12155748×10¹⁸112155748712800844C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
660151169151169C5.93954104×10¹⁰5939541048C3.92175232×10¹²392175232026C2.29709476×10¹⁵229709476535021C7.82038856×10¹⁸782038856708013244C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
67008.54260543×10¹⁰8542605432C1.25352360×10¹⁰1253523602C3.82117011×10¹⁵382117011299833C4.25984622×10¹⁸425984622389029784C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
680225192225192C1.22836380×10¹¹12283638000C1.00663300×10¹³1006633009506C6.40877102×10¹⁵640877102842629C2.87312120×10¹⁹2873121203862804519C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
69001.76593753×10¹¹17659375304C5.94765457×10¹⁰5947654570C1.10139028×10¹⁶1101390280743144C1.61600030×10¹⁹1616000309632165952C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
700335659335659C2.53829152×10¹¹25382915294C2.23873639×10¹³2238736398058C1.89900295×10¹⁶1899002957904670C1.05564525×10²⁰10556452527143724866C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
71003.64768808×10¹¹36476880888C8.02795365×10¹⁰8027953652C3.17330087×10¹⁶3173300871744772C6.12385216×10¹⁹6123852160220487036C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
720500161500161C5.24095349×10¹¹52409534930C5.72655937×10¹³5726559377337C5.34471346×10¹⁶5344713461113350C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
73007.52882823×10¹¹75288282340C3.53075095×10¹¹35307509572C9.15104391×10¹⁶9151043911619150C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
740745342745342C1.08136987×10¹²108136987218C1.27427734×10¹⁴12742773407214C1.57139758×10¹⁷15713975864851338C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
75001.55291596×10¹²155291596480C5.06510559×10¹¹50651055914C2.63533144×10¹⁷26353314485738146C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
76011107891110789C2.22972906×10¹²222972906692C3.24759746×10¹⁴32475974624227C4.45116834×10¹⁷44511683409170712C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
77003.20104649×10¹²320104649556C2.08566059×10¹²208566059216C7.60062507×10¹⁷76006250765774362C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
78016551871655187C4.59485571×10¹²459485571074C7.23492201×10¹⁴72349220121908C1.30128899×10¹⁸130128899926766052C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
79006.59464191×10¹²659464191528C3.15661411×10¹²315661411514C2.18851109×10¹⁸218851109395915798C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
80024667592466759C9.46351320×10¹²946351320390C1.83691507×10¹⁵183691507588209C3.70337271×10¹⁸370337271753041489C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
N>0x2kallallallallallallallall

See Also

I tetromino and C heptominoL tetromino and O tetromino