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 L hexomino

Prime rectangles: ≥ 53.

Smallest rectangle tilings

Smallest rectangle (4x8):

Smallest square (8x8):

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 \ h1-345678910N>0
1-30
4000
500000
60000000
7000000000
8022P000022P88C
90000000000000
1000000001616P196196P1616P144144P
11000000000104104C3232P4040P?
12000000044P2424C3232P224224P?
13000001616P00192192P640640P48244824P?
1401616P2020P000011081108C864864C7083270832C?
15000006464P100100P456456C616616P1753617536C?
16044C00002424C2138421384C11121112P117738117738C?
1700000192192P8080P1519215192C33243324P???
180000000252252C50405040C1046810468P???
1900000896896P176176P2220822208C2943629436P???
2009696P0022P41084108C142888142888C4432444324C???
210000033763376P27282728P101360101360C121000121000C???
2204848C0088P2870428704C22039342203934C495428495428C???
23000001094410944P1772017720C17259761725976C895104895104C???
24088C00312312P68046804C828088828088C16020641602064C???
25000003859238592P3050830508C26105662610566C66899286689928C???
260512512P0015681568C2377623776C1675484016754840C1157103011571030C???
2700000131968131968P9888498884C1548276015482760C1929150819291508C???
280384384C432432C57605760C7646876468C216035896216035896C4033288040332880C???
2900000428416428416P143596143596C180721518180721518C9737422097374220C???
300128128C200200P2752027520C692018692018C116160780116160780C260300642260300642C???
310000014068641406864P817012817012C304372872304372872C547509744547509744C???
32025762576C00113480113480C53373485337348C1.84885373×10¹⁰1848853730C1.14218428×10¹⁰1142184286C???
330000045761844576184C63174926317492C1.99893024×10¹⁰1998930242C2.81383051×10¹⁰2813830516C???
34025602560C00414128414128C2723359627233596C2.05001226×10¹¹20500122658C8.24427200×10¹⁰8244272008C???
35000001461011214610112C1964976019649760C1.81312020×10¹¹18131202080C1.56773188×10¹¹15677318832C???
36012801280C0015565601556560C1079718210797182C1.47082098×10¹¹14708209816C3.45315882×10¹¹34531588282C???
37000004658604846586048C3749159237491592C3.47554333×10¹¹34755433398C9.24117980×10¹¹92411798068C???
3801260812608C20482048P56982425698242C3912341039123410C1.95683754×10¹²195683754386C1.92009772×10¹²192009772648C???
3900000147711696147711696C9994857299948572C2.34840697×10¹²234840697048C4.03082603×10¹²403082603924C???
4001539215392C61446144P2000440420004404C156623540156623540C1.90472448×10¹³1904724483094C8.86928247×10¹²886928247194C???
4100000464500672464500672C292717512292717512C1.77397704×10¹³1773977048160C2.08042497×10¹³2080424977720C???
4201024010240C95369536C6959918469599184C1.09550248×10¹⁰1095502480C1.74073533×10¹³1740735333470C5.01481296×10¹³5014812964388C???
43000001.45655040×10¹⁰1456550408C1.54167681×10¹⁰1541676816C3.87344114×10¹³3873441147396C1.09139861×10¹⁴10913986167804C???
4406118461184C86408640C239526368239526368C5.71776990×10¹⁰5717769906C2.00868871×10¹⁴20086887102742C2.42547357×10¹⁴24254735705858C???
45000004.54988693×10¹⁰4549886936C7.38771959×10¹⁰7387719596C2.59803020×10¹⁴25980302095262C5.68253459×10¹⁴56825345979292C???
4608678486784C20002000P811128602811128602C2.14802155×10¹¹21480215584C1.74544345×10¹⁵174544345723248C1.42009806×10¹⁵142009806197248C???
47000001.41482475×10¹¹14148247564C1.89293026×10¹¹18929302600C1.70990128×10¹⁵170990128627614C2.99863182×10¹⁵299863182314188C???
4807174471744C002.71705216×10¹⁰2717052168C1.52840021×10¹¹15284002194C1.96419616×10¹⁵196419616736694C6.83956860×10¹⁵683956860985008C???
49000004.38818991×10¹¹43881899112C4.04501876×10¹¹40450187660C4.21594482×10¹⁵421594482975716C1.61119822×10¹⁶1611198222739344C???
500297984297984C009.03287612×10¹⁰9032876120C5.56651357×10¹¹55665135772C2.01472662×10¹⁶2014726628965772C3.61158422×10¹⁶3611584220847110C???
51000001.35732494×10¹²135732494192C1.16311277×10¹²116311277652C2.75818729×10¹⁶2758187290156814C8.06998484×10¹⁶8069984841273460C???
520469504469504C131072131072C2.97865423×10¹¹29786542328C2.44404600×10¹²244404600660C1.58527157×10¹⁷15852715744867626C1.81543527×10¹⁷18154352713189696C???
53000004.18627099×10¹²418627099208C4.44993565×10¹²444993565928C1.63366950×10¹⁷16336695033249422C4.17942074×10¹⁷41794207432301796C???
540460544460544C286720286720C9.74501629×10¹¹97450162920C1.30995633×10¹³1309956332640C2.13908700×10¹⁷21390870006299656C9.71766291×10¹⁷97176629187147258C???
55000001.28842836×10¹³1288428365032C1.98644241×10¹³1986442413608C4.49101582×10¹⁷44910158242992028C2.18868819×10¹⁸218868819701751552C???
56014664961466496C334592334592C3.17008091×10¹²317008091186C5.38310994×10¹³5383109942516C1.98506050×10¹⁸198506050914773376C4.93375584×10¹⁸493375584892144740C???
57000003.95742651×10¹³3957426516016C7.28696956×10¹³7286969562028C2.84296526×10¹⁸284296526534808806C1.13434807×10¹⁹1134348071594644228C???
58024739842473984C284032284032C1.02586228×10¹³1025862283080C1.65619365×10¹⁴16561936554902C1.43194938×10¹⁹1431949386059754456C2.66895007×10¹⁹2668950072432609106C???
59000001.21307969×10¹⁴12130796924136C1.77908043×10¹⁴17790804305956C1.55302811×10¹⁹1553028116473934614C5.94944934×10¹⁹5949449340386836636C???
60027811842781184C129600129600C3.30173569×10¹³3301735690760C1.95273848×10¹⁴19527384865310C2.26672092×10¹⁹2266720927446778152C1.35699895×10²⁰13569989581913825510C???
61000003.71228391×10¹⁴37122839195856C4.33329836×10¹⁴43332983674732C4.69412592×10¹⁹4694125928758792258C?????
62073113607311360C347680347680P1.05808565×10¹⁴10580856522864C7.26004692×10¹⁴72600469201692C???????
63000001.13426419×10¹⁵113426419180736C1.41615491×10¹⁵141615491246756C???????
6401282892812828928C851968851968P3.37785662×10¹⁴33778566214348C3.12745683×10¹⁵312745683400122C???????
65000003.46046851×10¹⁵346046851690568C5.59755163×10¹⁵559755163377656C???????
6601607270416072704C59965445996544C1.07417752×10¹⁵107417752299456C1.37597375×10¹⁶1375973759951188C???????
67000001.05433282×10¹⁶1054332827199904C2.16044035×10¹⁶2160440354516412C???????
6803690496036904960C1127219211272192C3.40466257×10¹⁵340466257548976C4.81309464×10¹⁶4813094645890910C???????
69000003.20835855×10¹⁶3208358554206456C6.82332223×10¹⁶6823322233397148C???????
7006593843265938432C1289113612891136C1.07594358×10¹⁶1075943580106290C1.33424844×10¹⁷13342484411597618C???????
71000009.75168915×10¹⁶9751689153611160C1.70962694×10¹⁷17096269422188320C???????
7208994867289948672C1019699210196992C3.39035694×10¹⁶3390356949128632C2.34603856×10¹⁷23460385692663190C???????
73000002.96081217×10¹⁷29608121736847984C4.74643888×10¹⁷47464388812452568C???????
740188153856188153856C56601605660160C1.06555843×10¹⁷10655584374382458C8.78617335×10¹⁷87861733590103516C???????
75000008.98064124×10¹⁷89806412410619472C1.66229754×10¹⁸166229754197561116C???????
760337563648337563648C2427238424272384C3.34108516×10¹⁷33410851629642652C3.54907468×10¹⁸354907468357124922C???????
77000002.72141839×10¹⁸272141839666526480C6.26842059×10¹⁸626842059442788972C???????
780491671552491671552C7858105678581056C1.04524131×10¹⁸104524131560703968C1.35350260×10¹⁹1353502607309057114C???????
790001677721616777216P8.23952833×10¹⁸823952833914209592C2.16807228×10¹⁹2168072283836069612C???????
800966067200966067200C262668288262668288C3.26321697×10¹⁸326321697442883232C4.27549636×10¹⁹4275496364516167024C???????
81000002.49259933×10¹⁹2492599337104653624C6.37667712×10¹⁹6376677127396600268C???????
8201.72656230×10¹⁰1726562304C438304768438304768C1.01682178×10¹⁹1016821788188495478C1.15665940×10²⁰11566594000181059718C???????
83000007.53471672×10¹⁹7534716722618789844C1.70243704×10²⁰17024370435547415500C???????
8402.64181350×10¹⁰2641813504C490647552490647552C???????????
8500000???????????
8604.98182963×10¹⁰4981829632C426174464426174464C???????????
8700000???????????
8808.83838361×10¹⁰8838383616C592541696592541696C???????????
8900000???????????
9001.40203786×10¹¹14020378624C1.38492825×10¹⁰1384928256C???????????
91000134217728134217728P???????????
9202.57478164×10¹¹25747816448C4.94571289×10¹⁰4945712896C???????????
93000671088640671088640C???????????
9404.53171937×10¹¹45317193728C1.11895194×10¹¹11189519488C???????????
95000335544320335544320P???????????
9607.37582817×10¹¹73758281728C1.71696455×10¹¹17169645568C???????????
9700000???????????
9801.33179506×10¹²133179506688C1.87318435×10¹¹18731843584C???????????
9900000???????????
10002.32764407×10¹²232764407808C2.01660334×10¹¹20166033408C???????????
10100000???????????
10203.85667514×10¹²385667514368C3.51011921×10¹¹35101192192C???????????
1030002.41591910×10¹⁰2415919104P???????????
10406.88824524×10¹²688824524800C8.74624368×10¹¹87462436864C???????????
1050009.66367641×10¹⁰9663676416C???????????
10601.19741664×10¹³1197416644608C2.45711350×10¹²245711350784C???????????
1070002.38907555×10¹¹23890755584C???????????
10802.00819887×10¹³2008198873088C4.75746472×10¹²475746472960C???????????
1090002.06695301×10¹¹20669530112C???????????
11003.56099286×10¹³3560992866304C6.80088644×10¹²680088644864C???????????
1110005.03316480×10¹⁰5033164800P???????????
11206.16731562×10¹³6167315628032C7.67863488×10¹²767863488512C???????????
11300000???????????
11401.04276287×10¹⁴10427628781568C1.00412211×10¹³1004122112000C???????????
1150008.58993459×10¹⁰8589934592P???????????
11601.83978081×10¹⁴18397808164864C1.93275309×10¹³1932753092608C???????????
1170001.99715979×10¹²199715979264C???????????
11803.17912482×10¹⁴31791248244736C4.96527844×10¹³4965278441472C???????????
1190006.30286450×10¹²630286450688C???????????
12005.40451463×10¹⁴54045146382336C1.13591227×10¹⁴11359122755584C???????????
1210009.64220157×10¹²964220157952C???????????
12209.49962460×10¹⁴94996246036480C1.99352300×10¹⁴19935230093312C???????????
1230009.14291163×10¹²914291163136C???????????
12401.63960609×10¹⁵163960609308672C2.73497015×10¹⁴27349701530624C???????????
1250004.18759311×10¹²418759311360C???????????
12602.79763082×10¹⁵279763082018816C3.35606133×10¹⁴33560613339648C???????????
1270001.78509578×10¹³1785095782400P???????????
12804.90274300×10¹⁵490274300166144C5.13370960×10¹⁴51337096069120C???????????
N>0x?allallallallallall

See Also

U pentomino and K hexominoU pentomino and N1 hexomino