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 pentomino and W pentomino

Prime rectangles: ≥ 48.

Smallest rectangle tilings

Smallest rectangle (12x15):

Smallest square (15x15):

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 \ h1-6789101112131415N>0
1-60
700
8000
90000
10000000000
1100000000
120000000000
13000000000000
1400000000000000
15000000000001212242436369696
1600000000000000352352?
1700000000000000≥1000≥1000?
1800000000000000≥1000≥1000?
1900000000000000≥1000≥1000?
20000000000154154≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
2100000000000000≥1000≥1000?
2200000000000000≥1000≥1000?
2300000000000000≥1000≥1000?
2400000000000000≥1000≥1000?
25000000000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000?
26000000???????????
27000000???????????
28000000???????????
29000000???????????
30022P44P66P88P???????????
3100001616P???????????
3200002828P???????????
3300004040P???????????
3400005252P???????????
3508686P180180P282282P456456P???????????
36000010121012P???????????
37000020402040P???????????
38000033483348P???????????
39000050325032P???????????
40019481948P43184318P71527152P1753817538P???????????
4100003956639566P???????????
4200008575885758P???????????
430000155990155990P???????????
440000262650262650P???????????
4503137231372P7454674546P132370132370P616876616876P???????????
46000013214061321406P???????????
47000028746962874696P???????????
48000055586005558600P???????????
4900001012826610128266P???????????
500407648407648P10506961050696P20309102030910P2059875220598752P???????????
5100004168293841682938P???????????
5200008766284887662848P???????????
530000173514834173514834P???????????
540000330756744330756744P???????????
55045831564583156P1295549812955498P2768590627685906P645421442645421442P???????????
5600001.26425306×10¹⁰1264253068P???????????
5700002.56184264×10¹⁰2561842648P???????????
5800005.07019369×10¹⁰5070193694P???????????
5900009.84820217×10¹⁰9848202176P???????????
6004655591446555914C145781912145781912C349438178349438178C1.90610413×10¹¹19061041394C???????????
N>0x5k5k5kall?????

See Also

I pentomino and V pentominoI pentomino and Y pentomino