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 Z pentomino

Prime rectangles: ≥ 62.

Smallest rectangle tilings

Smallest rectangle (10x16):

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 \ h1-8910111213141516N>0
1-80
900
1000000
1100000
12000000
130000000
1400000000
1500000707019619632232244844811481148
16001212P0000≥1≥100
17002424P0000≥1≥100?
18003636P0000≥1≥100?
19004848P0000≥1≥100?
200006060P831283122996429964≥1≥1≥1≥1≥1≥1≥1≥1?
2100436436P0000≥1≥100?
220010281028P0000≥1≥100?
230018841884P0000≥1≥100?
240030523052P0000≥1≥100?
2500045804580P547616547616≥1000≥1000≥1≥1≥1≥1≥1≥1≥1≥1?
26001320413204P0000≥1≥100?
27003103831038P0000≥1≥100?
28006301263012P0000≥1≥100?
2900115466115466P0000≥1≥100?
30000196324196324P≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1≥1?
3100414150414150P0000≥1≥100?
3200890532890532C0000≥1≥100?
330018339861833986C0000?????
340035613363561336C0000?????
3500065330226533022C?????????????
36001270054412700544C0000?????
37002551781025517810C0000?????
38005134086051340860C0000?????
3900101068552101068552C0000?????
40000192450324192450324C?????????????
4100369344562369344562C0000?????
4200719756504719756504C0000?????
43001.41464257×10¹⁰1414642576C0000?????
44002.76978258×10¹⁰2769782584C0000?????
45022P5.34188075×10¹⁰5341880758C?????????????
46001.02641281×10¹¹10264128166C0000?????
47001.97954846×10¹¹19795484688C0000?????
48003.83736075×10¹¹38373607522C0000?????
49007.44801485×10¹¹74480148560C0000?????
500122122P1.43797907×10¹²143797907378C?????????????
51002.76563799×10¹²276563799384C0000?????
52005.31635662×10¹²531635662426C0000?????
53001.02366262×10¹³1023662623204C0000?????
54001.97373570×10¹³1973735703126C0000?????
55039183918P3.80033973×10¹³3800339736258C?????????????
56007.30204192×10¹³7302041922884C0000?????
57001.40129697×10¹⁴14012969789710C0000?????
58002.68917327×10¹⁴26891732758742C0000?????
59005.16341945×10¹⁴51634194509846C0000?????
6008875288752P9.91142600×10¹⁴99114260014450C?????????????
61001.90078092×10¹⁵190078092339442C0000?????
62003.64186846×10¹⁵364186846956668C0000?????
63006.97449485×10¹⁵697449485637046C0000?????
64001.33562941×10¹⁶1335629410806158C0000?????
65016023301602330P2.55741589×10¹⁶2557415892041214C?????????????
66004.89477664×10¹⁶4894776643543304C0000?????
67009.36305317×10¹⁶9363053178135872C0000?????
68001.79018613×10¹⁷17901861324789088C0000?????
69003.42190835×10¹⁷34219083574904166C0000?????
7002468615224686152P6.53969089×10¹⁷65396908998823072C?????????????
71001.24948769×10¹⁸124948769567526504C0000?????
72002.38645226×10¹⁸238645226629383658C0000?????
7300≥1≥1C0000?????
7400≥1≥1C0000?????
750339087718339087718P≥1≥1C?????????????
7600≥1≥1C0000?????
7700≥1≥1C0000?????
7800≥1≥1C0000?????
7900≥1≥1C0000?????
8004.28007955×10¹⁰4280079550P≥1≥1C?????????????
8100≥1≥1C0000?????
8200≥1≥1C0000?????
8300≥1≥1C0000?????
8400≥1≥1C0000?????
8505.07296101×10¹¹50729610128P≥1≥1C?????????????
8600≥1≥1C0000?????
8700≥1≥1C0000?????
8800≥1≥1C0000?????
8900≥1≥1C0000?????
9005.73537066×10¹²573537066548C≥1≥1C?????????????
9100≥1≥1C0000?????
9200≥1≥1C0000?????
9300≥1≥1C0000?????
9400≥1≥1C0000?????
9506.25641528×10¹³6256415288224C≥1≥1C?????????????
9600≥1≥1C0000?????
9700≥1≥1C0000?????
9800≥1≥1C0000?????
9900≥1≥1C0000?????
10006.64018944×10¹⁴66401894409950C≥1≥1C?????????????
N>0x5kall5k5k5k5kall?

See Also

I pentomino and Y pentominoI pentomino and A hexomino