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.


L tetromino and U pentomino

Prime rectangles: ≥ 27.

Smallest rectangle tilings

Smallest rectangle (3x6):

Smallest square (6x6):

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 \ h1-23456789N>0
1-20
3000
400000
50000000
6022P004040P88C
7000003232P240240P44564456P
8000002424P212212C11321132P2026820268P
9044P0014161416P64526452C3247632476P167056167056C18501601850160C
100000026442644P47744774C255302255302C15406781540678C5265491452654914Call
11088P3232P28802880P6009260092C514004514004C1081399810813998C354597420354597420Call
1201212C0039823982C7612476124C37229083722908C9152566091525660C2.64618813×10¹⁰2646188132Call
13000194194P78127812C13161781316178C3361544433615444C686978150686978150C4.43550306×10¹¹44355030652Call
1403636P100100P6883068830C16459681645968C249776778249776778C5.18631125×10¹⁰5186311258C2.70298741×10¹²270298741744Call
1503232C13261326P245492245492C1307384213073842C1.19990721×10¹⁰1199907212C3.76692492×10¹¹37669249272C3.01454974×10¹³3014549746900Call
16000640640P575190575190C2614609026146090C3.22232823×10¹⁰3222328230C2.75197515×10¹²275197515678C2.32863970×10¹⁴23286397034450Call
170112112C81428142P34031083403108C257426040257426040C2.01985073×10¹¹20198507340C1.97029716×10¹³1970297161474C2.02214385×10¹⁵202214385757760Call
1808888C44804480P98708469870846C475844036475844036C9.06482984×10¹¹90648298444C1.40097182×10¹⁴14009718268676C2.57528839×10¹⁶2575288397145022Call
1909696P4605446054P2257903222579032C2.69868366×10¹⁰2698683664C4.45644370×10¹²445644370288C9.91200121×10¹⁴99120012187008C1.98707056×10¹⁷19870705633556136Call
200368368C2760827608P4306654443066544C7.07212217×10¹⁰7072122178C2.92779075×10¹³2927790753566C6.94653072×10¹⁵694653072829078C1.94353682×10¹⁸194353682111169844Call
210240240C251836251836P7940816079408160C4.96240392×10¹¹49624039270C1.74559431×10¹⁴17455943194700C4.86513161×10¹⁶4865131619573886C1.91128322×10¹⁹1911283220381333216Call
220456456C158888158888C225937332225937332C1.17916416×10¹²117916416918C9.06705860×10¹⁴90670586091086C3.38374206×10¹⁷33837420644070318C1.55461888×10²⁰15546188855476045886Call
23011521152C13321301332130P787520880787520880C5.50031377×10¹²550031377628C4.24381827×10¹⁵424381827053924C2.35427167×10¹⁸235427167128281656C≥1≥1Call
240656656C878336878336C2.46635016×10¹⁰2466350162C1.68531005×10¹³1685310051746C1.80828219×10¹⁶1808282193610344C1.62869146×10¹⁹1628691469449803650C≥1≥1Call
25017761776C68794966879496C9.89072001×10¹⁰9890720016C9.56705024×10¹³9567050249522C9.14872471×10¹⁶9148724714022160C1.12808192×10²⁰11280819237767103074C≥1≥1Call
26035683568C47030684703068C3.05899861×10¹¹30589986128C2.66884131×10¹⁴26688413151254C4.64547205×10¹⁷46454720592907992C≥1≥1C≥1≥1Call
27026562656C3485115034851150C8.40434437×10¹¹84043443704C1.11878385×10¹⁵111878385560314C2.55417309×10¹⁸255417309370688572C≥1≥1C≥1≥1Call
28066726672C2459731224597312C2.07505905×10¹²207505905230C3.74014759×10¹⁵374014759813032C1.41210131×10¹⁹1412101312337739284C≥1≥1C≥1≥1Call
2901088010880C173856702173856702C4.72188952×10¹²472188952464C1.85516023×10¹⁶1855160234271066C7.34799410×10¹⁹7347994105790884096C≥1≥1C≥1≥1Call
30096489648C126238472126238472C1.11548171×10¹³1115481711044C5.73325244×10¹⁶5733252444416148C≥1≥1C≥1≥1C≥1≥1Call
N>0xallallallallallallall

Smallest prime reptiles

Smallest prime reptiles (4Lx3, 5Ux4):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
L tetromino004P2123P≥1P≥1P≥1P
U pentomino00069701P≥1P≥1P≥1P

Smallest common multiples

Smallest common multiple (area 20):

Common multiples' solutions count (excluding symmetric)

area20
solutions≥2P

See Also

L tetromino and T pentominoL tetromino and V pentomino