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 X pentomino

Prime rectangles: ≥ 23.

Smallest rectangle tilings

Smallest rectangle (5x6):

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 \ h1-45678910N>0
1-40
5000
6044P22P
70000000
8000000000
9000424424P000000
1003232P208208C1428814288P136136P230672230672P13568461356846C
110002424C00466466P00124653460124653460C?
1201616C44C32403240P64646464P27734982773498C1923915619239156C?
130005584855848P002512425124P005.48436858×10¹⁰5484368586C?
14037203720P2745627456C15550601555060P226816226816P4.68291631×10¹⁰4682916314P1.39450791×10¹¹13945079126C?
1500067286728C0013381501338150P001.36255894×10¹³1362558948464C?
160272272C760760C14396721439672P1089889610898896P7.19972252×10¹⁰7199722520C3.73284706×10¹²373284706922C?
1700076219607621960C006305036463050364P007.66591455×10¹⁴76659145575280C?
1806321663216C37952403795240C1.68735222×10¹⁰1687352220P440659642440659642P7.38892669×10¹³7388926694870C1.62216498×10¹⁵162216498225280C?
1900015963061596306C002.71679907×10¹⁰2716799070P001.56444744×10¹⁷15644474452197708C?
2002523225232C154624154624C1.06613176×10¹⁰1066131768C1.84592759×10¹¹18459275992C5.28727844×10¹⁴52872784484074C5.66929416×10¹⁶5669294167083844C?
210001.06080419×10¹⁰1060804192C001.14106220×10¹²114106220656C009.35868375×10¹⁸935868375639722754C?
22046168304616830C534480960534480960C2.54588019×10¹²254588019520C7.45836015×10¹²745836015922C5.15876043×10¹⁷51587604348192114C1.93058807×10¹⁹1930588076473312442C?
23000324752424324752424C004.64695893×10¹³4646958937534C00≥1.84467440×10²⁰≥18446744073709551615C?
240662892662892C3163644831636448C3.24455583×10¹²324455583676C2.98164536×10¹⁴29816453661440C1.34690934×10¹⁸134690934055633192C≥1.84467440×10²⁰≥18446744073709551615C?
250001.49186594×10¹²149186594056C001.85572528×10¹⁵185572528305948C00≥1.84467440×10²⁰≥18446744073709551615C?
2609426568294265682C7.59583244×10¹¹75958324470C2.00365557×10¹⁵200365557638792C1.17386161×10¹⁶1173861618257528C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
270005.97155308×10¹¹59715530820C007.29281107×10¹⁶7292811075483842C00≥1.84467440×10²⁰≥18446744073709551615C?
2804079528440795284C6.19160631×10¹⁰6191606312C1.85904557×10¹⁵185904557640346C4.56802192×10¹⁷45680219240158920C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
290002.10615264×10¹⁴21061526495648C002.82895010×10¹⁸282895010867031292C00≥1.84467440×10²⁰≥18446744073709551615C?
3005.44345964×10¹⁰5443459640C1.08281093×10¹⁴10828109314412C3.37935387×10¹⁷33793538727814670C1.75895853×10¹⁹1758958532123338716C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
310001.02664211×10¹⁴10266421103196C001.08565290×10²⁰10856529083507377478C00≥1.84467440×10²⁰≥18446744073709551615C?
3201.17568696×10¹⁰1175686962C1.15080283×10¹³1150802830672C5.40077804×10¹⁷54007780455884430C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
330002.97399547×10¹⁶2973995472503962C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
3401.24466730×10¹²124466730744C1.54329691×10¹⁶1543296911998576C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
350001.68486749×10¹⁶1684867498689834C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
3605.99170691×10¹¹59917069122C2.04400292×10¹⁵204400292665072C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
370004.19297473×10¹⁸419297473740444016C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
3806.25011479×10¹³6250114796360C2.19577436×10¹⁸219577436429497066C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
390002.67449783×10¹⁸267449783126781388C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
4001.80233881×10¹³1802338810684C3.49880552×10¹⁷34988055264042446C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
41000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
4201.53897840×10¹⁵153897840176068C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
43000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
4408.25677114×10¹⁴82567711488658C5.81504621×10¹⁹5815046219083136292C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
45000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
4607.03630106×10¹⁶7036301061619814C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
47000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
4802.53837988×10¹⁶2538379881008766C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
49000≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C00≥1.84467440×10²⁰≥18446744073709551615C?
5001.82585880×10¹⁸182585880850889344C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C≥1.84467440×10²⁰≥18446744073709551615C?
N>0x??????

See Also

L tetromino and W pentominoL tetromino and Y pentomino