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 W pentomino

Prime rectangles: ≥ 83.

Smallest rectangle tilings

Smallest rectangle (8x11):

Smallest square (12x12):

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 \ h1-5678910111213141516N>0
1-50
6000
700000
80000000
9000000000
1000000000000
110000022P003232P00
120000044P4646P118118P608608P≥1000≥1000P
130000066P0022P00≥1000≥1000P176176P
140000088P0000≥1000≥1000P≥1000≥1000P≥1000≥1000P≥1≥1P
1500000120120P0036323632P116116P≥1000≥1000P≥1000≥1000P≥1≥1P≥1≥1P
16022P44P270270P35363536P1593615936P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C
1700044P462462P168168P734734P≥1000≥1000P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C?
1800000705705P106106P218218P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1P≥1≥1C≥1≥1C?
1900044P34463446P2020P253326253326P≥1000≥1000P≥1000≥1000C≥1000≥1000P≥1≥1C≥1≥1C≥1≥1C?
2003434P7676P84338433P164686164686P11986691198669P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C?
21000116116P1659616596P2076820768P102704102704P≥4000≥4000P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
2200022P2941629416C1259612596P4145841458C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
23000132132P8564685646C25162516P1433557414335574C?????????????
240366366P948948P208046208046C63341646334164C6989020069890200C?????????????
2500019481948P442484442484C14143681414368P95923949592394C?????????????
26000166166P869974869974C846740846740P44767824476782C?????????????
2700024162416P20569262056926C175232175232P726999960726999960C?????????????
28032583258P1020610206P47575844757584C220643320220643320C3.56611651×10¹⁰3566116515C?????????????
290002564425644P1036126210361262C7123048471230484C718897868718897868C?????????????
3000061626162P2153613621536136C4261036842610368C367025670367025670C?????????????
310003312433124P4740067447400674C90690849069084C3.45882188×10¹¹34588218894C?????????????
3202634426344C104024104024C105170137105170137C7.21462449×10¹⁰7214624494C1.68490730×10¹²168490730539C?????????????
33022P300520300520C228435042228435042C2.98930390×10¹⁰2989303904C4.68139895×10¹¹46813989584C?????????????
34000146064146064C485268987485268987C1.79811980×10¹⁰1798119802C2.55801622×10¹¹25580162200C?????????????
35000384800384800C1.04434307×10¹⁰1044343072C395375764395375764C1.58070747×10¹³1580707475070C?????????????
360201642201642C10330221033022C2.26223592×10¹⁰2262235922C2.25550502×10¹²225550502236C7.58811024×10¹³7588110245304C?????????????
3709090P33284043328404C4.86940590×10¹⁰4869405901C1.11402715×10¹²111402715180C2.75930485×10¹³2759304855644C?????????????
3800026019262601926C1.03883446×10¹¹10388344656C6.76381028×10¹¹67638102878C1.60269564×10¹³1602695643482C?????????????
3900040416244041624C2.21797808×10¹¹22179780882C1.55415803×10¹¹15541580304C7.02981103×10¹⁴70298110370372C?????????????
40014902541490254C1003535810035358C4.74592882×10¹¹47459288245C6.81993314×10¹³6819933148262C3.30943047×10¹⁵330943047949542C?????????????
41021502150P3561864435618644C1.01352369×10¹²101352369259C3.83006261×10¹³3830062610052C1.50889589×10¹⁵150889589830812C?????????????
420003816116638161166C2.15724702×10¹²215724702664C2.35350480×10¹³2353504801368C9.31049976×10¹⁴93104997614097C?????????????
430003984315639843156C4.58545698×10¹²458545698132C5.72574677×10¹²572574677628C3.06534697×10¹⁶3065346970052898C?????????????
4401074492610744926C9521773895217738C9.74678916×10¹²974678916803C2.01025905×10¹⁵201025905426798C1.41079512×10¹⁷14107951215707109C?????????????
4503648636486P369900304369900304C2.06980839×10¹³2069808399570C1.24458963×10¹⁵124458963275592C7.78511887×10¹⁶7785118875260172C?????????????
46000487590892487590892C4.38910101×10¹³4389101016227C7.75658620×10¹⁴77565862071632C5.10989208×10¹⁶5109892086933099C?????????????
47000376971684376971684C9.29621902×10¹³9296219026602C2.02012362×10¹⁴20201236249212C1.31669002×10¹⁸131669002182683786C?????????????
4807603632676036326C882072070882072070C1.96765580×10¹⁴19676558058508C5.80907208×10¹⁶5809072087300810C5.91300108×10¹⁸591300108068809216C?????????????
490496060496060C3.72753827×10¹⁰3727538272C4.16176258×10¹⁴41617625891428C3.88380264×10¹⁶3883802645876128C3.83671998×10¹⁸383671998972391524C?????????????
50044P5.63279723×10¹⁰5632797238C8.79488766×10¹⁴87948876646029C2.45920223×10¹⁶2459202230931238C2.68252748×10¹⁸268252748783306560C?????????????
51022P3.46997247×10¹⁰3469972472C1.85703680×10¹⁵185703680204812C6.90492778×10¹⁵690492778461672C5.58854794×10¹⁹5588547942394649588C?????????????
520530184736530184736C7.99223859×10¹⁰7992238594C3.91836290×10¹⁵391836290182169C1.65245535×10¹⁸165245535388697154C???????????????
53057716285771628C3.64838940×10¹¹36483894028C8.26260891×10¹⁵826260891063028C1.17630076×10¹⁸117630076418752924C???????????????
540220220P6.03520147×10¹¹60352014794C1.74116694×10¹⁶1741166949655774C7.57814772×10¹⁷75781477254759338C???????????????
550114114P3.13465502×10¹¹31346550204C3.66685382×10¹⁶3666853824026172C2.30077933×10¹⁷23007793346190740C???????????????
5603.65294725×10¹⁰3652947254C7.10635180×10¹¹71063518072C7.71768708×10¹⁶7717687085626978C4.64136678×10¹⁹4641366782955781122C???????????????
5705988725659887256C3.47762823×10¹²347762823476C1.62348368×10¹⁷16234836850893472C3.48307664×10¹⁹3483076644478788076C???????????????
58063446344P6.10681948×10¹²610681948580C3.41324887×10¹⁷34132488702459012C2.28557057×10¹⁹2285570572319114526C???????????????
59033903390P2.79611746×10¹²279611746660C7.17247635×10¹⁷71724763549439960C7.50063408×10¹⁸750063408918491508C???????????????
6002.49215131×10¹¹24921513166C6.22650314×10¹²622650314026C1.50645854×10¹⁸150645854764405144C?????????????????
610569782182569782182C3.23993828×10¹³3239938283704C3.16262350×10¹⁸316262350164117422C?????????????????
620128128128128P5.91355560×10¹³5913555608180C6.63644178×10¹⁸663644178220781689C?????????????????
6307028670286P2.47463511×10¹³2474635113356C1.39199396×10¹⁹1391993960632145410C?????????????????
6401.68616940×10¹²168616940310C5.40067781×10¹³5400677812310C???????????????????
6505.06905388×10¹⁰5069053888C2.96141093×10¹⁴29614109367432C???????????????????
66020421962042196C5.53526593×10¹⁴55352659351302C???????????????????
67011453201145320C2.18198738×10¹⁴21819873847244C???????????????????
6801.13277466×10¹³1132774665324C4.65908350×10¹⁴46590835043966C???????????????????
6904.27730224×10¹¹42773022498C2.66490340×10¹⁵266490340301392C???????????????????
7002743382427433824C5.04743559×10¹⁵504743559562688C???????????????????
7101567109815671098C1.92382583×10¹⁵192382583080632C???????????????????
7207.56320457×10¹³7563204570992C4.01586134×10¹⁵401586134304096C???????????????????
7303.45965370×10¹²345965370626C2.36811349×10¹⁶2368113497344004C???????????????????
740323839488323839488C4.51199490×10¹⁶4511994904371408C???????????????????
750187775960187775960C1.70138319×10¹⁶1701383199607712C???????????????????
7605.02239176×10¹⁴50223917626260C3.47267678×10¹⁶3472676782352198C???????????????????
7702.70391037×10¹³2703910372706C2.08345238×10¹⁷20834523898753608C???????????????????
7803.45710067×10¹⁰3457100670C3.97454712×10¹⁷39745471260198850C???????????????????
7902.02831038×10¹⁰2028310386C1.51287662×10¹⁷15128766234861952C???????????????????
8003.31910613×10¹⁵331910613055664C3.02275874×10¹⁷30227587402011646C???????????????????
8102.05457311×10¹⁴20545731181952C1.81879029×10¹⁸181879029650004020C???????????????????
8203.40802974×10¹¹34080297460C3.46532009×10¹⁸346532009740094656C???????????????????
8302.01707366×10¹¹20170736628C1.35472753×10¹⁸135472753134229480C???????????????????
8402.18402392×10¹⁶2184023928414692C2.65456772×10¹⁸265456772574455650C???????????????????
8501.52511819×10¹⁵152511819151814C1.57846589×10¹⁹1578465897180559448C???????????????????
8603.15161303×10¹²315161303240C3.00184937×10¹⁹3001849376000488608C???????????????????
8701.87616479×10¹²187616479330C1.22257975×10¹⁹1222579754672133380C???????????????????
8801.43154871×10¹⁷14315487143014978C2.35470296×10¹⁹2354702962406973990C???????????????????
8901.11015129×10¹⁶1110151290768962C1.36424876×10²⁰13642487628812893968C???????????????????
9002.76738397×10¹³2767383970260C≥1≥1C???????????????????
9101.65222636×10¹³1652226368096C≥1≥1C???????????????????
9209.35035648×10¹⁷93503564878082584C≥1≥1C???????????????????
9307.94823827×10¹⁶7948238276060122C≥1≥1C???????????????????
9402.32941757×10¹⁴23294175753572C≥1≥1C???????????????????
9501.39077956×10¹⁴13907795639920C≥1≥1C???????????????????
9606.08784207×10¹⁸608784207663886000C≥1≥1C???????????????????
9705.61086946×10¹⁷56108694649875568C≥1≥1C???????????????????
9801.89386316×10¹⁵189386316722900C≥1≥1C???????????????????
9901.12751623×10¹⁵112751623702822C≥1≥1C???????????????????
N>0xallallallallallallallallallallall

See Also

I tetromino and V pentominoI tetromino and X pentomino