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 R pentomino

Prime rectangles: 59.

Smallest rectangle tilings

Smallest rectangle and 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 \ h1-45678910111213141516N>0
1-40
5000
600022P
70000000
8000000000
900000000000
100002828P0022P4444P23042304P
11000000044P4848P412412P144144P
120001010C2020P3636P290290P34943494C92189218P≥1000≥1000C
130000088P8282P556556P69746974P1748417484P≥1000≥1000C761920761920P
14000268268P88P262262P44284428P≥1000≥1000C138204138204P≥1000≥1000C≥1000≥1000C≥1≥1C
15044P66P00510510P90529052P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C
16000208208C464464P16581658P3158831588P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1C
1700088P220220P40704070P7499674996P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
18022P22822282C348348P1195911959P341830341830P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1906868P132132P248248P2727027270P919912919912P≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
20022P27022702C72867286P6885168851C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
21000??39923992P??????????????????all
2203636P??94729472P??????????????????all
230688688P??1008010080P??????????????????all
2404040P??≥10000≥10000C??????????????????all
25044P??≥1≥1C??????????????????all
260400400P??≥1≥1C??????????????????all
27054765476P??≥1≥1C??????????????????all
280464464P??≥1≥1C??????????????????all
2909696P??≥1≥1C??????????????????all
30035943594C??≥1≥1C??????????????????all
3103816838168P??????????????????????all
32041904190P??????????????????????all
33013281328C??????????????????????all
3402864628646C??????????????????????all
350245712245712C??????????????????????all
3603318633186C??????????????????????all
3701417614176C??????????????????????all
380210996210996C??????????????????????all
39015046161504616C??????????????????????all
400244014244014C??????????????????????all
410130664130664C??????????????????????all
42014687881468788C??????????????????????all
43089152688915268C??????????????????????all
44017092861709286C??????????????????????all
45010957401095740C??????????????????????all
46098057329805732C??????????????????????all
4705164790051647900C??????????????????????all
4801153793011537930C??????????????????????all
49085835288583528C??????????????????????all
5006342767263427672C??????????????????????all
N>0xallallallallallallallallallallallall

See Also

I tetromino and P pentominoI tetromino and T pentomino