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 X pentomino

Prime rectangles: ≥ 13.

Smallest rectangle tilings

Smallest rectangle (3x5):

Smallest square (15x15):

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 \ h1-2345678910111213141516171819202122232425262728N>0
1-20
300
4000
5011P00
600011C0
7000000
80000000
900011C0000
10011C0011C0011C0
110000000000
1200011C000011C00
13000000000000
140000000000000
15011C011C11C022C11C11C33C11C33C44C22C
16000000000000066C0
17000000000000055C00
1800011C000011C000055C000
1900000000000001010C0000
20011C0011C0011C0011C0077C0001717C0000
2100011C000011C00001111C00003333C0
2200000000000001515C0000000??
2300000000000001212C0000000????
2400011C000011C00002121C00005757C0??????
25011C0011C0011C0011C002222C0004949C00008585C????????
2600000000000002323C0000000??????????
2700011C000011C00003636C00009191C0????????????
2800000000000003434C0000000??????≥1≥1P??????
2900000000000004444C0000000???????????????
30011C011C11C044C11C11C99C11C99C1616C5858C3636C2525C137137C100100C173173C297297C???????????????
3100000000000005757C0000000???????????????
3200000000000008080C0000000???????????????
3300011C000011C00009292C0000355355C0???????????????
340000000000000101101C0000000???????????????
35011C0011C0011C0011C00138138C000375375C0000954954C??≥1≥1P????????≥1≥1P?
3600011C000011C0000149149C0000725725C0???????????????
370000000000000181181C0000000???????????????
380000000000000230230C0000000??????≥1≥1P???????
3900011C000011C0000250250C000014291429C0???????????????
40011C0011C0011C0011C00319319C00010291029C88P0028632863C??≥1≥1P???????????
410000000000000379379C0000000???????????????
4200011C000011C0000431431C000026892689C0???????????????
430000000000000549549C0000000???????????????
440000000000000629629C0000000???????????????
45011C011C11C088C11C11C2727C11C2727C6464C750750C216216C125125C28592859C10001000C50435043C90289028C???????????????
460000000000000928928C0000000???????????????
47000000000000010601060C0000000???????????????
4800011C000011C000012991299C000096139613C0???????????????
49000000000000015571557C0000000???????????????
50011C0011C0011C0011C0018101810C00079857985C00002859928599C≥1≥1P?????????????
5100011C000011C000022272227C00001860918609C0???????????????
52000000000000026172617C0000000???????????????
53000000000000031093109C0000000???????????????
5400011C000011C000037843784C00003623736237C0???????????????
55011C0011C0011C0011C0044274427C0002228922289C224224C008913389133C???????????????
56000000000000053365336C0000000???????????????
5700011C000011C000064016401C00007011570115C0???????????????
58000000000000075367536C0000000???????????????
59000000000000091209120C0000000???????????????
60011C011C11C01616C11C11C8181C11C8181C256256C1082810828C12961296C627627C6212162121C1000010000C134729134729C279181279181C???????????????
6100000000000001287212872C0000000???????????????
6200000000000001552115521C0000000???????????????
63000??0000??00001836418364C0000258261258261C0???????????????
6400000000000002199221992C0000000???????????????
65011C00??0011C0011C002634926349C000172989172989C3232P00877835877835C???????????????
66000??0000??00003123631236C0000495835495835C0???????????????
6700000000000003751337513C0000000???????????????
6800000000000004471344713C0000000???????????????
69000??0000??00005322853228C0000954827954827C0???????????????
70011C00??00??0011C006386263862C000481661481661C44504450C22P27544902754490C???????????????
7100000000000007594975949C000022P0???????????????
72000??0000??00009074190741C000018411351841135C0???????????????
730000000000000108575108575C000088C0???????????????
740000000000000129177129177C00002020C0???????????????
75011C0????03232C????243243C11C243243C10241024C154603154603C77767776C31533153C13413431341343C100000100000C35483133548313C86478258647825C???????????????
760000000000000184524184524C00001414C0???????????????
770000000000000219918219918C00003838C0???????????????
78000??0000??0000263178263178C000068307436830743C0???????????????
790000000000000313701313701C00002828C0???????????????
80011C00??00??0011C00374521374521C00037359733735973C704704C6262C2718732927187329C???????????????
81000??0000??0000447702447702C00001314075513140755C0???????????????
820000000000000533619533619C00004444C0???????????????
830000000000000637699637699C00009090C0???????????????
84000??0000??0000761403761403C00002528255525282555C0???????????????
85011C00??00??0011C00908140908140C03838P1040606310406063C7403274032C180180C8548074885480748C???????????????
86000000000000010854011085401C0000154154C0???????????????
87000??0000??000012950221295022C00004866502348665023C0???????????????
88000000000000015458391545839C0000424424C0???????????????
89000000000000018468041846804C0000686686C0???????????????
90011C0????06464C????729729C11C729729C40964096C22031622203162C4665646656C1589115891C2898426128984261C10002561000256C9370111393701113C268795742268795742C???????????????
91000000000000026312402631240C0000832832C0???????????????
92000000000000031418263141826C000016201620C0???????????????
93000??0000??000037490013749001C0000180415211180415211C0???????????????
94000000000000044780444478044C000016641664C0???????????????
95011C00??00??0011C0053449885344988C0008072876180728761C1256012560C33283328C845533550845533550C???????????????
96000??0000??000063802416380241C0000347318287347318287C0???????????????
97000000000000076198707619870C000030523052C0???????????????
98000000000000090939899093989C000062346234C0???????????????
99000??0000??00001085828510858285C0000668532591668532591C0???????????????
100011C00??00??0011C001296485812964858C0778778C224848577224848577C11015861101586C76567656C2.66019017×10¹⁰2660190171C???????????????
10100000000000001547423015474230C00001129211292C0???????????????
102000??0000??00001847815518478155C00001.28679727×10¹⁰1286797275C0???????????????
10300000000000002205884722058847C00001687816878C0???????????????
10400000000000002633251526332515C00002632426324C0???????????????
105011C0????0128128C????21872187C11C21872187C1638416384C3144301331443013C279936279936C8025980259C626256337626256337C1001011210010112C2.47699042×10¹⁰2476990429C8.37032606×10¹⁰8370326064C???????????????
10600000000000003753307737533077C00003515635156C0???????????????
10700000000000004481067044810670C00005771057710C0???????????????
108000??0000??00005350186053501860C00004.76830889×10¹⁰4768308897C0???????????????
10900000000000006386559263865592C00007131471314C0???????????????
110011C00??00??0011C007625368376253683C02020P1.74427689×10¹⁰1744276897C214592214592C122196122196C2.63414861×10¹¹26341486181C???????????????
111000??0000??00009103493791034937C00009.17932380×10¹⁰9179323805C0???????????????
1120000000000000108676262108676262C0000139124139124C0???????????????
1130000000000000129755543129755543C0000248072248072C0???????????????
114000??0000??0000154900529154900529C00001.76704540×10¹¹17670454091C0???????????????
115011C00??00??0011C00184929945184929945C096469646C4.85824613×10¹⁰4858246135C1519045615190456C294508294508C8.29082702×10¹¹82908270238C???????????????
1160000000000000220790480220790480C0000487712487712C0???????????????
117000??0000??0000263576791263576791C00003.40152623×10¹¹34015262331C0???????????????
1180000000000000314685488314685488C0000613328613328C0???????????????
1190000000000000375691009375691009C000010033541003354C0???????????????
120011C0????0256256C????65616561C11C65616561C6553665536C448506736448506736C16796161679616C406185406185C1.35314308×10¹¹13531430853C100276480100276480C6.54781103×10¹¹65478110307C2.60978451×10¹²260978451655C???????????????
1210000000000000535475968535475968C000012688921268892C0???????????????
1220000000000000639267800639267800C000020614022061402C0???????????????
123000??0000??0000763192224763192224C00001.26043783×10¹²126043783641C0???????????????
1240000000000000911166977911166977C000025851022585102C0???????????????
125011C00??00??0011C001.08777453×10¹⁰1087774536C0882882C3.76884070×10¹¹37688407027C36049463604946C42309364230936C8.21599466×10¹²821599466852C???????????????
126000??0000??00001.29866819×10¹⁰1298668192C00002.42633782×10¹²242633782287C0???????????????
12700000000000001.55043477×10¹⁰1550434777C000051694285169428C0???????????????
12800000000000001.85096676×10¹⁰1850966760C000085972968597296C0???????????????
129000??0000??00002.20983516×10¹⁰2209835169C00004.67071245×10¹²467071245717C0???????????????
130011C00??00??0011C002.63820931×10¹⁰2638209313C09410094100C1.04971574×10¹²104971574121C198370314198370314C1049928610499286C2.58678991×10¹³2586789919035C???????????????
13100000000000003.14963495×10¹⁰3149634952C00001726817017268170C0???????????????
132000??0000??00003.76026994×10¹⁰3760269946C00008.99112730×10¹²899112730849C0???????????????
13300000000000004.48917607×10¹⁰4489176073C00002124336821243368C0???????????????
13400000000000005.35947012×10¹⁰5359470121C00003480764434807644C0???????????????
135011C0????0512512C????1968319683C11C1968319683C262144262144C6.39847925×10¹⁰6398479259C1007769610077696C20597632059763C2.92371878×10¹²292371878641C1.00606851×10¹⁰1006068512C1.73078576×10¹³1730785767741C8.14521863×10¹³8145218633125C???????????????
13600000000000007.63881102×10¹⁰7638811025C00004306077043060770C0???????????????
13700000000000009.11974006×10¹⁰9119740067C00007008074470080744C0???????????????
138000??0000??00001.08876553×10¹¹10887655332C00003.33174285×10¹³3331742855835C0???????????????
13900000000000001.29982811×10¹¹12998281146C00008693399686933996C0???????????????
140011C00??00??0011C001.55182193×10¹¹15518219326C01881618816C8.14328246×10¹²814328246537C5914975659149756C141125236141125236C2.56496684×10¹⁴25649668487890C???????????????
141000??0000??00001.85264663×10¹¹18526466357C00006.41356997×10¹³6413569975419C0???????????????
14200000000000002.21180212×10¹¹22118021213C0000174274846174274846C0???????????????
14300000000000002.64058746×10¹¹26405874658C0000283510154283510154C0???????????????
144000??0000??00003.15247475×10¹¹31524747503C00001.23460754×10¹⁴12346075435817C0???????????????
145011C00??00??0011C003.76362405×10¹¹37636240539C0796232796232C2.26810637×10¹³2268106378421C2.48846988×10¹⁰2488469888C349904428349904428C8.07784249×10¹⁴80778424922566C???????????????
14600000000000004.49323410×10¹¹44932341015C0000567901778567901778C0???????????????
147000??0000??00005.36427687×10¹¹53642768716C00002.37661317×10¹⁴23766131788567C0???????????????
14800000000000006.40421151×10¹¹64042115197C0000700415476700415476C0???????????????
14900000000000007.64570885×10¹¹76457088518C00001.13592184×10¹⁰1135921840C0???????????????
150011C0????010241024C????5904959049C11C5904959049C10485761048576C9.12790092×10¹¹91279009255C6046617660466176C1046598910465989C6.31723960×10¹³6317239600933C1.01145196×10¹¹10114519608C4.57496789×10¹⁴45749678918083C2.54413782×10¹⁵254413782665585C???????????????
15100000000000001.08974456×10¹²108974456212C00001.40236315×10¹⁰1402363156C0???????????????
15200000000000001.30099857×10¹²130099857234C00002.26880093×10¹⁰2268800930C0???????????????
153000??0000??00001.55321124×10¹²155321124452C00008.80678351×10¹⁴88067835191283C0???????????????
15400000000000001.85431544×10¹²185431544730C00002.80509964×10¹⁰2805099646C0???????????????
155011C00??00??0011C002.21378866×10¹²221378866489C0277578277578C1.75950813×10¹⁴17595081318703C939499380939499380C4.52845910×10¹⁰4528459102C8.01336576×10¹⁵801336576304196C???????????????
156000??0000??00002.64295580×10¹²264295580664C00001.69529927×10¹⁵169529927610147C0???????????????
15700000000000003.15531401×10¹²315531401964C00005.59640322×10¹⁰5596403228C0???????????????
15800000000000003.76699990×10¹²376699990941C00009.02693837×10¹⁰9026938374C0???????????????
159000??0000??00004.49727125×10¹²449727125394C00003.26343836×10¹⁵326343836252961C0???????????????
160011C00??00??0011C005.36910268×10¹²536910268453C061330346133034C4.90066713×10¹⁴49006671320517C3.02841504×10¹¹30284150466C1.11601810×10¹¹11160181028C2.52415585×10¹⁶2524155851834523C???????????????
16100000000000006.40995571×10¹²640995571605C00001.79754615×10¹¹17975461516C0???????????????
162000??0000??00007.65258527×10¹²765258527358C00006.28209592×10¹⁵628209592049325C0???????????????
16300000000000009.13610259×10¹²913610259394C00002.22127282×10¹¹22212728226C0???????????????
16400000000000001.09072269×10¹³1090722696999C00003.57477799×10¹¹35747779968C0???????????????
165011C0????020482048C????177147177147C11C177147177147C41943044194304C1.30216879×10¹³1302168795811C362797056362797056C5329859753298597C1.36495750×10¹⁵136495750233239C1.01939427×10¹²101939427680C1.20929930×10¹⁶1209299302460127C7.95137374×10¹⁶7951373741532088C???????????????
16600000000000001.55460583×10¹³1554605830999C00004.41787959×10¹¹44178795934C0???????????????
16700000000000001.85598122×10¹³1855981224357C00007.10154695×10¹¹71015469556C0???????????????
168000??0000??00002.21577905×10¹³2215779055205C00002.32789324×10¹⁶2327893240298463C0???????????????
16900000000000002.64532852×10¹³2645328527998C00008.78154732×10¹¹87815473236C0???????????????
170011C00??00??0011C003.15815002×10¹³3158150020168C032656583265658C3.80174562×10¹⁵380174562315197C1.43882323×10¹¹14388232392C1.40976762×10¹²140976762016C2.50490390×10¹⁷25049039049164342C???????????????
171000??0000??00003.77038488×10¹³3770384886204C00004.48117885×10¹⁶4481178858012935C0???????????????
17200000000000004.50130975×10¹³4501309752355C00001.74325653×10¹²174325653822C0???????????????
17300000000000005.37392907×10¹³5373929075373C00002.79599335×10¹²279599335334C0???????????????
174000??0000??00006.41571341×10¹³6415713414202C00008.62623843×10¹⁶8626238436076743C0???????????????
175011C00??00??0011C007.65945977×10¹³7659459772523C04420783044207830C1.05888057×10¹⁶1058880570865529C3.60064025×10¹²360064025768C3.45837088×10¹²345837088118C7.89152883×10¹⁷78915288367552993C???????????????
17600000000000009.14431396×10¹³9144313961577C00005.54135700×10¹²554135700012C0???????????????
177000??0000??00001.09170231×10¹⁴10917023166557C00001.66054493×10¹⁷16605449347045247C0???????????????
17800000000000001.30333888×10¹⁴13033388847896C00006.85348977×10¹²685348977126C0???????????????
17900000000000001.55600273×10¹⁴15560027375779C00001.09719409×10¹³1097194093978C0???????????????
180011C0????040964096C????531441531441C11C531441531441C1677721616777216C1.85764829×10¹⁴18576482939080C2.17678233×10¹⁰2176782336C272221943272221943C2.94924536×10¹⁶2949245360366817C1.03033425×10¹³1030334255730C3.19653759×10¹⁷31965375945828155C2.48628436×10¹⁸248628436247050008C???????????????
18100000000000002.21777028×10¹⁴22177702809473C00001.35709855×10¹³1357098552992C0???????????????
18200000000000002.64770505×10¹⁴26477050542336C00002.17071910×10¹³2170719104488C0???????????????
183000??0000??00003.16098717×10¹⁴31609871786976C00006.15331314×10¹⁷61533131453036689C0???????????????
18400000000000003.77377301×10¹⁴37737730185252C00002.68580634×10¹³2685806340330C0???????????????
185011C00??00??0011C004.50535334×10¹⁴45053533481416C03298340832983408C8.21438076×10¹⁶8214380768378409C2.12504483×10¹²212504483590C4.29209560×10¹³4292095601720C7.83354837×10¹⁸783354837142020672C???????????????
186000??0000??00005.37875745×10¹⁴53787574596449C00001.18450861×10¹⁸118450861323923921C0???????????????
18700000000000006.42147807×10¹⁴64214780727588C00005.31082489×10¹³5310824891270C0???????????????
18800000000000007.66634052×10¹⁴76663405268392C00008.48073043×10¹³8480730435582C0???????????????
189000??0000??00009.15253047×10¹⁴91525304781701C00002.28017103×10¹⁸228017103886255123C0???????????????
190011C00??00??0011C001.09268314×10¹⁵109268314209004C0303424822303424822C2.28790904×10¹⁷22879090465349097C4.20397030×10¹³4203970306586C1.04949941×10¹⁴10494994185334C2.46821484×10¹⁹2468214847208875846C???????????????
19100000000000001.30450979×10¹⁵130450979864841C00001.67474339×10¹⁴16747433960012C0???????????????
192000??0000??00001.55740085×10¹⁵155740085509289C00004.38931374×10¹⁸438931374926222303C0???????????????
19300000000000001.85931719×10¹⁵185931719477396C00002.07256612×10¹⁴20725661290386C0???????????????
19400000000000002.21976284×10¹⁵221976284646542C00003.30491049×10¹⁴33049104963306C0???????????????
195011C0????081928192C????15943231594323C11C15943231594323C6710886467108864C2.65008399×10¹⁵265008399718293C1.30606940×10¹¹13060694016C1.39643407×10¹⁰1396434071C6.37239489×10¹⁷63723948917717639C1.04470544×10¹⁴10447054451624C8.44939904×10¹⁸844939904010002243C7.77719185×10¹⁹7777191856652242340C???????????????
19600000000000003.16382699×10¹⁵316382699342237C00004.09034279×10¹⁴40903427927510C0???????????????
19700000000000003.77716370×10¹⁵377716370155831C00006.51781479×10¹⁴65178147931884C0???????????????
198000??0000??00004.50940119×10¹⁵450940119195689C00001.62650355×10¹⁹1626503558911928643C0???????????????
19900000000000005.38358983×10¹⁵538358983988779C00008.06860574×10¹⁴80686057432240C0???????????????
200011C00??00??0011C006.42724769×10¹⁵642724769874124C0298685688298685688C1.77487023×10¹⁸177487023430823109C3.03410530×10¹³3034105306404C1.28480420×10¹⁵128480420737130C≥1.84467440×10²⁰≥18446744073709551615C???????????????
N>0x5kx3k5kx15k5k3k15k5k15k15kall15k5k5k5kall5k???????

Attributions

  1. Prime rectangle list taken from http://www.recmath.com/PolyPages/PolyPages/index.htm?5pairs.htm

See Also

U pentomino and V pentominoU pentomino and Y pentomino