POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

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You may also see list of all polyomino sets for which data is available here.


A 9-omino

Area: 9.

Size: 3x4.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 4.

Odd order: ≤ 247.

Prime rectangles: ≥ 17.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

Smallest known odd rectangle (19x117):

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 \ h1-234-567-8910111213141516171819N>0
1-20
300
4-5000
6022P088C
7-800000
90002424C00
100000000
1100000000
12044C08080C0704704C0092169216C
130000000000
1400000000000
15000256256C00009728097280C0000
1600000000000000
170000000000000000
18088C0832832C02099220992C0011509761150976C00003876454438764544C3232P001.76370483×10¹⁰1763704832C
190000000000000000512512C0
200000000000000000520520P0?
2100026882688C00001279590412795904C00000006.61211095×10¹¹66121109504C0?
2200000000000000009625696256C0?
23000000000000000083208320C0?
2401616C087048704C0626688626688C00147128320147128320C001.55440917×10¹¹15544091712C0002.80328834×10¹³2803288344576C0?
25000000000000000024908802490880C0?
26000000000000000017287681728768C0?
270002816028160C00001.66094438×10¹⁰1660944384C0000040964096P001.09788907×10¹⁵109788907398144C00?
280000000000000000212603392212603392C0?
2900000000000000004358041643580416C0?
3003232C09113691136C01871052818710528C001.89383311×10¹¹18938331136C006.23847446×10¹³6238474461696C0004.52381753×10¹⁶4523817530568832C0?
3100000000000000007.23313254×10¹⁰7233132544C0?
3200000000000000004.00220774×10¹⁰4002207744C0?
33000294912294912C00002.14769336×10¹²214769336320C00000001.80404112×10¹⁸180404112444086784C0?
3400000000000000004.33168864×10¹²433168864768C0?
3500000000000000001.32364567×10¹²132364567552C0?
3606464C0954368954368C0558628864558628864C256256P02.44277942×10¹³2442779426816C3276832768C002.50407063×10¹⁶2504070631497216C2.71707750×10¹⁰2717077504C237568237568P7.34699236×10¹⁹7346992366444880384C7.91405378×10¹²791405378560C?
3700000000000000001.69366536×10¹⁴16936653623296C0?
3800000000000000008.31512029×10¹³8315120293376C0?
3900030883843088384C00002.77395160×10¹⁴27739516043264C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
4000000000000000008.56126559×10¹⁵856126559467584C0?
4100000000000000003.18922745×10¹⁵318922745692160C0?
420128128C099942409994240C01.66786498×10¹¹16678649856C003.15277443×10¹⁵315277443072000C001.00513121×10¹⁹1005131212529944576C000≥1.84467440×10²⁰≥18446744073709551615C0?
4300000000000000003.56158569×10¹⁷35615856920540672C0?
4400000000000000001.65813630×10¹⁷16581363029921792C0?
450003234201632342016C00003.58162798×10¹⁶3581627988967424C000003.29720012×10¹⁰3297200128C00≥1.84467440×10²⁰≥18446744073709551615C00?
4600000000000000001.65705434×10¹⁹1657054349987590656C0?
4700000000000000006.82874701×10¹⁸682874701643261952C0?
480256256C0104660992104660992C04.97964548×10¹²497964548096C004.06986848×10¹⁷40698684895133696C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
490000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
500000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
51000338690048338690048C00004.62401418×10¹⁸462401418947461120C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
520000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
530000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
540512512C01.09602406×10¹⁰1096024064C01.48674319×10¹⁴14867431948288C005.25401363×10¹⁹5254013633268023296C40964096P00≥1.84467440×10²⁰≥18446744073709551615C2.26306361×10¹²226306361344C2.81451724×10¹¹28145172480P≥1.84467440×10²⁰≥18446744073709551615C1.33762826×10¹⁶1337628263546880C?
550000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
560000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
570003.54680832×10¹⁰3546808320C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
580000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
590000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
600??01.14777128×10¹¹11477712896C04.43888091×10¹⁵443888091267072C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
610000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
620000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
630003.71426590×10¹¹37142659072C0000≥1.84467440×10²⁰≥18446744073709551615C000005.11067137×10¹⁴51106713733120C00≥1.84467440×10²⁰≥18446744073709551615C00?
640000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
650000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
66020482048C01.20196169×10¹²120196169728C01.32529032×10¹⁷13252903275855872C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
670000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
680000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
690003.88962975×10¹²388962975744C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
700000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
710000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
72040964096C01.25871063×10¹³1258710630400C03.95684066×10¹⁸395684066986295296C6553665536C0≥1.84467440×10²⁰≥18446744073709551615C1.68021196×10¹⁰1680211968C5033164850331648P≥1.84467440×10²⁰≥18446744073709551615C8.87488332×10¹⁹8874883328981436416C4.52474955×10¹⁷45247495599726592C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
730000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
740000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
750004.07327316×10¹³4073273163776C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
760000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
770000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
78081928192C01.31813888×10¹⁴13181388849152C01.18137043×10²⁰11813704333906673664C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
790000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
800000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
810004.26558703×10¹⁴42655870353408C0000≥1.84467440×10²⁰≥18446744073709551615C02.28170137×10¹⁰2281701376P00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00?
820000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
830000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
8401638416384C01.38037296×10¹⁵138037296103424C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
850000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
860000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
870004.46698073×10¹⁵446698073620480C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
880000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
890000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
9003276832768C01.44554533×10¹⁶1445545331654656C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C2.20620390×10¹⁰2206203904C1.17037858×10¹²117037858816P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
910000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
920000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
930004.67788295×10¹⁶4677882957791232C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
940000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
950000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
9606553665536C01.51379472×10¹⁷15137947242201088C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
970000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
980000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
990004.89874263×10¹⁷48987426315567104C0000≥1.84467440×10²⁰≥18446744073709551615C05.45782969×10¹³5457829691392P00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00?
1000000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1010000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1020131072131072C01.58526641×10¹⁸158526641599938560C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
1030000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1040000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1050005.13002988×10¹⁸513002988462145536C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1060000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1070000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1080262144262144C01.66011254×10¹⁹1660112543324045312C0≥1.84467440×10²⁰≥18446744073709551615C1677721616777216C0≥1.84467440×10²⁰≥18446744073709551615C8.73875604×10¹⁴87387560476672C2.56557723×10¹⁵256557723942912P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
1090000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1100000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1110005.37223704×10¹⁹5372237040496672768C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1120000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1130000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1140524288524288C01.73849242×10²⁰17384924254289526784C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
1150000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1160000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
117000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C01.18867600×10¹⁷11886760078344192P00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615P?
1180000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1190000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
120010485761048576C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
1210000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1220000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
123000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1240000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1250000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
126020971522097152C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C1.07312791×10¹⁶1073127912112128C5.46310124×10¹⁸546310124835176448P≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
1270000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1280000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
129000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1300000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1310000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
132041943044194304C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
1330000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1340000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
135000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615P00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
1360000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1370000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
138083886088388608C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
1390000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1400000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
141000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1420000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1430000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
14401677721616777216C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C4.29496729×10¹⁰4294967296C0≥1.84467440×10²⁰≥18446744073709551615C5.14152108×10¹⁹5141521080359321600C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
1450000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1460000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
147000≥1.84467440×10²⁰≥18446744073709551615C0000≥1.84467440×10²⁰≥18446744073709551615C0000000≥1.84467440×10²⁰≥18446744073709551615C0?
1480000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
1490000000000000000≥1.84467440×10²⁰≥18446744073709551615C0?
15003355443233554432C0≥1.84467440×10²⁰≥18446744073709551615C0≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C000≥1.84467440×10²⁰≥18446744073709551615C0?
N>0x6kx3kx6k36kx3k18k9k?9k?all9k

Smallest prime reptiles

Smallest prime reptile (9Ax6):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
A 9-omino10000≥736624640P

See Also

P3 octominoB1 9-omino