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 G hexomino

Prime rectangles: ≥ 66.

Smallest rectangle tilings

Smallest rectangle (10x12):

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 \ h1-78910111213N>0
1-70
8000
90000
100000000
110000000
120000022P44P1212P
1300000002828P00
14000000044P≥1≥1P≥1≥1P?
150000000≥1≥1P00?
1600022P224224P514514P≥1≥1P≥1≥1P?
17000088P0≥1≥1P00?
180000088P340340P≥1≥1P≥1≥1P?
190000000≥1≥1P00?
20000114114P1404214042P3879438794P≥1≥1C≥1≥1P?
210000668668P0??00?
2200044P948948P2214422144P??≥1≥1P?
2300004848P0??00?
2400044524452P693926693926C23822742382274C??≥1≥1C?
2500003564435644P0??00?
26000320320P6336063360P13006081300608C?????
27022P034883488P0?????
28044P152188152188P3049654030496540C132075594132075594C?????
29066P016062041606204C0?????
30088P1494814948P32768143276814C7105878871058788C?????
3106060P0174832174832P0?????
320144144P48448864844886C1.25354261×10¹⁰1253542610C6.89236646×10¹⁰6892366466C?????
330268268P06675401266754012C0?????
340442442P553808553808P148133648148133648C3.68467109×10¹⁰3684671092C?????
35014341434P076544567654456C0?????
36035523552P146965702146965702C4.93751114×10¹¹49375111448C3.45601742×10¹²345601742976C?????
37074587458P02.64679351×10¹⁰2646793516C0?????
3801408614086P1824924418249244C6.19694788×10¹⁰6196947880C1.84097698×10¹²184097698952C?????
3903383233832P0313314420313314420C0?????
4007958279582P4.30628288×10¹⁰4306282888C1.88844902×10¹³1888449021250C1.68486627×10¹⁴16848662747000C?????
410174196174196P01.01708600×10¹²101708600544C0?????
420354768354768P562935688562935688C2.46941204×10¹²246941204788C8.95426086×10¹³8954260864836C?????
430776282776282P01.23071014×10¹¹12307101496C0?????
44017327401732740P1.23031804×10¹²123031804024C7.06945649×10¹⁴70694564940184C8.04509945×10¹⁵804509945261048C?????
45037914523791452P03.82114400×10¹³3821144009412C0?????
46079827827982782P1.66629730×10¹¹16662973052C9.52266078×10¹³9522660788480C4.26877634×10¹⁵426877634499612C?????
4701705155017051550P04.69925694×10¹²469925694372C0?????
4803692611036926110P3.44930143×10¹³3449301439388C2.60362917×10¹⁶2603629171323320C3.78080070×10¹⁷37808007050327294C?????
4907982543479825434P01.41129394×10¹⁵141129394218300C0?????
500169702980169702980P4.79513804×10¹²479513804856C3.58677412×10¹⁵358677412892560C2.00386282×10¹⁷20038628285366372C?????
510360439984360439984P01.75744028×10¹⁴17574402881596C0?????
520769452660769452660P9.53059947×10¹⁴95305994758956C9.46676488×10¹⁷94667648869995470C1.75460440×10¹⁹1754604402513275810C?????
5301.64523091×10¹⁰1645230914P05.14330601×10¹⁶5143306015347060C0?????
5403.49627288×10¹⁰3496272888C1.35180375×10¹⁴13518037539148C1.32731181×10¹⁷13273118162971338C9.29214789×10¹⁸929214789194739760C?????
5507.40771036×10¹⁰7407710368C06.46891916×10¹⁵646891916139220C0?????
5601.57068970×10¹¹15706897068C2.60306597×10¹⁶2603065972168598C3.40667838×10¹⁹3406678383336600258C≥1.84467440×10²⁰≥18446744073709551615C?????
5703.33367434×10¹¹33336743424C01.85441829×10¹⁸185441829561029488C0?????
5807.06091328×10¹¹70609132828C3.75145558×10¹⁵375145558905776C4.84468061×10¹⁸484468061671502044C≥1.84467440×10²⁰≥18446744073709551615C?????
5901.49235341×10¹²149235341294C02.35146000×10¹⁷23514600011162000C0?????
6003.15215537×10¹²315215537788C7.04303534×10¹⁷70430353465492198C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
6106.65863850×10¹²665863850598C06.62747344×10¹⁹6627473446330707300C0?????
6201.40545261×10¹³1405452610050C1.02824669×10¹⁷10282466913018356C1.74892977×10²⁰17489297716530528016C≥1.84467440×10²⁰≥18446744073709551615C?????
6302.96282750×10¹³2962827501870C08.46132819×10¹⁸846132819994951308C0?????
6406.24081092×10¹³6240810920424C1.89076774×10¹⁹1890767745009470050C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
6501.31408642×10¹⁴13140864264562C0≥1.84467440×10²⁰≥18446744073709551615C0?????
6602.76561945×10¹⁴27656194571030C2.79018535×10¹⁸279018535423328940C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
6705.81614333×10¹⁴58161433374868C0≥1.84467440×10²⁰≥18446744073709551615C0?????
6801.22230910×10¹⁵122230910289398C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
6902.56757153×10¹⁵256757153481056C0≥1.84467440×10²⁰≥18446744073709551615C0?????
7005.39110334×10¹⁵539110334349866C7.50872698×10¹⁹7508726980049045136C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
7101.13137550×10¹⁶1131375509987674C0≥1.84467440×10²⁰≥18446744073709551615C0?????
7202.37304384×10¹⁶2373043844736584C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
7304.97518014×10¹⁶4975180149534796C0≥1.84467440×10²⁰≥18446744073709551615C0?????
7401.04265255×10¹⁷10426525532846992C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
7502.18419612×10¹⁷21841961224124246C0≥1.84467440×10²⁰≥18446744073709551615C0?????
7604.57363070×10¹⁷45736307098123806C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
7709.57325577×10¹⁷95732557781483116C0≥1.84467440×10²⁰≥18446744073709551615C0?????
7802.00310034×10¹⁸200310034648948948C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
7904.18980739×10¹⁸418980739994348226C0≥1.84467440×10²⁰≥18446744073709551615C0?????
8008.76060953×10¹⁸876060953115415976C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
8101.83116874×10¹⁹1831168740652012682C0≥1.84467440×10²⁰≥18446744073709551615C0?????
8203.82635188×10¹⁹3826351889764572622C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
8307.99299082×10¹⁹7992990826399143968C0≥1.84467440×10²⁰≥18446744073709551615C0?????
8401.66918503×10²⁰16691850386740204338C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
850≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
860≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
870≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
880≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
890≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
900≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
910≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
920≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
930≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
940≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
950≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
960≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
970≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
980≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
990≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C0?????
1000≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?????
N>0xall2kall2k??

See Also

I tetromino and C hexominoI tetromino and T1 hexomino