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 A hexomino

Prime rectangles: ≥ 6.

Smallest rectangle tilings

Smallest rectangle and smallest square (4x4):

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 \ h1-23456789101112N>0
1-20
3000
400088P
50001616P00
60002424P0000
70006666P000000
8066P164164C524524C13441344C81908190C6147461474C
9000340340C000000259102259102C00
10000696696C000000951048951048C0000
1100014881488C00000048004084800408C000000
1203232P32683268C1595415954C6079060790C10325801032580C2746525027465250C212294070212294070C1.35755876×10¹⁰1357558763C1.73582213×10¹¹17358221302C2.90308511×10¹²290308511210C
1300069946994C000000126927316126927316C0000002.74304022×10¹³2743040225282C?
140001458014580C000000541767960541767960C0000002.25732953×10¹⁴22573295377609C?
150003083030830C0000002.61115267×10¹⁰2611152676C0000002.59183664×10¹⁵259183664358110C?
160136136C6609266092C480138480138C26916822691682C132269562132269562C1.33995246×10¹¹13399524650C1.79255973×10¹²179255973334C1.95814675×10¹³1958146750050C6.54685039×10¹⁴65468503978766C3.47229633×10¹⁶3472296339601014C?
17000140448140448C0000006.35880257×10¹¹63588025780C0000003.57235201×10¹⁷35723520131821788C?
18000296296296296C0000002.89603519×10¹²289603519884C0000003.35161781×10¹⁸335161781334729746C?
19000627374627374C0000001.37992167×10¹³1379921676562C0000003.68941857×10¹⁹3689418578568306352C?
200538538C13331801333180C1442223014422230C118889530118889530C1.70142181×10¹¹17014218186C6.77460293×10¹³6774602931716C1.52557340×10¹⁵152557340540404C2.83052980×10¹⁶2830529806874716C2.50655888×10¹⁸250655888026420818C≥1.84467440×10²⁰≥18446744073709551615C?
2100028286342828634C0000003.23395112×10¹⁴32339511251052C000000≥1.84467440×10²⁰≥18446744073709551615C?
2200059890245989024C0000001.51344501×10¹⁵151344501620046C000000≥1.84467440×10²⁰≥18446744073709551615C?
230001268717812687178C0000007.19875592×10¹⁵719875592336942C000000≥1.84467440×10²⁰≥18446744073709551615C?
24020662066C2690764026907640C433074694433074694C5.24968619×10¹⁰5249686198C2.19097490×10¹³2190974908470C3.47152359×10¹⁶3471523596972668C1.30088851×10¹⁸130088851029713974C4.09344517×10¹⁹4093445173709941642C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
250005705515657055156C0000001.65783642×10¹⁷16578364268596430C000000≥1.84467440×10²⁰≥18446744073709551615C?
26000120901452120901452C0000007.84514569×10¹⁷78451456919680176C000000≥1.84467440×10²⁰≥18446744073709551615C?
27000256208896256208896C0000003.73332902×10¹⁸373332902506066290C000000≥1.84467440×10²⁰≥18446744073709551615C?
28078247824C543131372543131372C1.30038097×10¹¹13003809760C2.31796406×10¹²231796406116C2.82211382×10¹⁵282211382319428C1.78756104×10¹⁹1787561046321350300C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
290001.15135853×10¹⁰1151358532C0000008.53116763×10¹⁹8531167632116623814C000000≥1.84467440×10²⁰≥18446744073709551615C?
300002.44027074×10¹⁰2440270748C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
310005.17203226×10¹⁰5172032264C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
3202942429424C1.09628763×10¹¹10962876376C3.90458236×10¹²390458236512C1.02347662×10¹⁴10234766202620C3.63527736×10¹⁷36352773608562630C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
330002.32376967×10¹¹23237696770C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
340004.92539221×10¹¹49253922128C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
350001.04396028×10¹²104396028924C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
360110258110258C2.21277717×10¹²221277717012C1.17240567×10¹⁴11724056793976C4.51906794×10¹⁵451906794969698C4.68280991×10¹⁹4682809916647935684C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
370004.69023463×10¹²469023463006C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
380009.94136738×10¹²994136738628C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
390002.10715059×10¹³2107150592116C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
400412378412378C4.46629749×10¹³4466297496972C3.52031174×10¹⁵352031174387740C1.99535318×10¹⁷19953531840827122C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
410009.46675245×10¹³9466752452900C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
420002.00656445×10¹⁴20065644546084C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
430004.25308851×10¹⁴42530885160326C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
44015407921540792C9.01480497×10¹⁴90148049710976C1.05702270×10¹⁷10570227027962082C8.81029965×10¹⁸881029965827507324C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
450001.91077130×10¹⁵191077130016674C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
460004.05005386×10¹⁵405005386857644C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
470008.58445295×10¹⁵858445295894544C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
48057538645753864C1.81955244×10¹⁶1819552448331752C3.17385807×10¹⁸317385807375566890C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
490003.85670730×10¹⁶3856707308604118C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
500008.17464171×10¹⁶8174641719361328C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
510001.73268929×10¹⁷17326892910115530C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
5202148081021480810C3.67259194×10¹⁷36725919487522900C9.52995146×10¹⁹9529951467395974222C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
530007.78439221×10¹⁷77843922128655690C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
540001.64997260×10¹⁸164997260231574056C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
550003.49726653×10¹⁸349726653153627376C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
5608018166680181666C7.41277354×10¹⁸741277354883225216C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
570001.57120462×10¹⁹1571204620414963576C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
580003.33031076×10¹⁹3330310768685564368C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
590007.05889576×10¹⁹7058895764919677824C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
600299270432299270432C1.49619698×10²⁰14961969869024669664C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
61000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
62000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
63000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
6401.11694921×10¹⁰1116949216C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
65000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
66000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
67000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
6804.16862473×10¹⁰4168624738C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
69000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
70000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
71000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
7201.55577463×10¹¹15557746346C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
73000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
74000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
75000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
7605.80627538×10¹¹58062753864C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
77000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
78000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
79000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C000000≥1.84467440×10²⁰≥18446744073709551615C?
8002.16694055×10¹²216694055544C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
N>0x??????????

See Also

I tetromino and Z pentominoI tetromino and C hexomino