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.


O tetromino and T pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest rectangle (8x10):

Smallest square (10x10):

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 \ h1-7891011121314151617N>0
1-70
8000
90000
10011044
1100000000
1202201313003636
1300000000171700
140330262600717100156156
15000000008888000000
16055058580026326300107410740076167616
17000000002132130000000000
1807701421421010881881626626412241229518951846060460608054680546?
1900000000120312030000000000?
2001010029829800207920790013771137710029516029516000?
2100000000455145510000000000?
220151506946940089368936009574395743002109603210960300?
230000000010842108420000000000?
2402121017691769380380316543165439445394454120404120401382704138270413435954134359544066001540660015?
250000000049001490010000000000?
2603030039563956007726477264001583581158358100882877078828770700?
27000000001805181805180000000000?
28043430934593450031905231905200980581498058140061330627861330627800?
29000000004573924573920000000000?
30060600235222352295049504114079511407952554050255405044773115447731152149906702149906704.01549223×10¹⁰40154922322.14695253×10¹¹21469525308?
3100000000189763918976390000000000?
320858505423254232002946988294698800187901730187901730002.65951667×10¹¹2659516677300?
3300000000683031568303150000000000?
3401201200128846128846001182522011825220001.05793789×10¹⁰1057937899001.81460242×10¹²18146024248000?
350000000018071861180718610000000000?
360168168032051232051223239223239242160826421608261641005191641005194.95989327×10¹⁰49598932743.40464966×10¹¹340464966761.20479350×10¹³12047935046961.15242168×10¹⁴11524216823328?
370000000071753430717534300000000000?
380237237075282675282600113635104113635104002.20319815×10¹¹22031981562008.02342934×10¹³802342934938900?
39000000002559758512559758510000000000?
40033333301794569179456900442151618442151618001.16868245×10¹²116868245337005.42263924×10¹⁴5422639245070400?
N>0x?x????????

See Also

O tetromino and P pentominoO tetromino and V pentomino