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.


L1 9-omino

Area: 9.

Size: 2x8.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 36.

Odd order: 33.

Prime rectangles: ≥ 12.

Smallest rectangle tilings

Smallest rectangle (2x9):

Smallest square (18x18):

Smallest odd rectangle (11x27):

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 \ h123456789101112131415161718192021222324N>0
10
200
3000
40000
500000
6000000
70000000
800000000
9022P044C088C01616C0
10000000003232C0
1100000000000
12000000006464C0000
130000000000000
1400000000128128C00000
1500000000000000000
1600000000256256C0000000
1700000000000000000
18044C01616C06464C0256256C512512C10321032C61446144C41684168C4300843008C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C
1900000000000000000≥1≥1C0
200000000010241024C00000000≥1≥1C00
210000000000000000000≥1≥1C00??
220000000020482048C00000000≥1≥1C0000
2300000000000000000≥1≥1C00000
240000000040964096C0000000000≥1≥1C00≥1≥1P00??
2500000000000000000≥1≥1C00000???
260000000081928192C00000000≥1≥1C00000???
27088C06464C0512512C040964096C03328033280C10241024P272384272384C1843218432C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?
28000000001638416384C00000000≥1≥1C00000???
2900000000000000000≥1≥1C00000???
30000000003276832768C000000??00≥1≥1C00≥1≥1P00???
3100000000000000000≥1≥1C00000???
32000000006553665536C00000000≥1≥1C00000???
33000000000000000??00≥1≥1C00≥1≥1P00???
3400000000131072131072C00000000≥1≥1C00000???
3500000000000000000≥1≥1C00000???
3601616C0256256C040964096C06553665536C262144262144C10733601073360C3778156837781568C1781510417815104C1.85103462×10¹⁰1851034624C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C???????
3700000000000000000≥1≥1C00000???
3800000000524288524288C00000000≥1≥1C00000???
39000000000000000??00≥1≥1C00≥1≥1P00???
400000000010485761048576C00000000≥1≥1C00000???
4100000000000000000≥1≥1C00000???
420000000020971522097152C000000??00≥1≥1C00≥1≥1C00???
4300000000000000000≥1≥1C00000???
440000000041943044194304C00000000≥1≥1C00000???
4503232C010241024C03276832768C010485761048576C03463219234632192C1259110412591104C1.16621721×10¹⁰1166217216C1.58636441×10¹⁰1586364416C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C???????
460000000083886088388608C00000000≥1≥1C00000???
4700000000000000000≥1≥1C00000???
48000000001677721616777216C000000??00≥1≥1C00≥1≥1C00???
4900000000000000000≥1≥1C00000???
50000000003355443233554432C00000000≥1≥1C00000???
510000000000081928192P00??00≥1≥1C00≥1≥1C00???
52000000006710886467108864C00000000≥1≥1C00000???
5300000000000000000≥1≥1C00000???
5406464C040964096C0262144262144C01677721616777216C134217728134217728C1.11844019×10¹⁰1118440192C2.32333320×10¹²232333320704C7.64881024×10¹¹76488102400C7.97364014×10¹⁴79736401461248C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C???????
5500000000000000000≥1≥1C00000???
5600000000268435456268435456C00000000≥1≥1C00000???
57000000000000000??00≥1≥1C00≥1≥1C00???
5800000000536870912536870912C00000000≥1≥1C00000???
5900000000000000000≥1≥1C00000???
60000000001.07374182×10¹⁰1073741824C0026255362625536C00??00≥1≥1C00≥1≥1C00???
6100000000000000000≥1≥1C00000???
62000000002.14748364×10¹⁰2147483648C00000000≥1≥1C00000???
630128128C01638416384C020971522097152C0268435456268435456C03.61900113×10¹¹36190011392C1.16140515×10¹²116140515328C5.03650510×10¹³5036505104384C1.03038460×10¹⁵103038460362752C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
64000000004.29496729×10¹⁰4294967296C00000000≥1≥1C00000???
6500000000000000000≥1≥1C00000???
66000000008.58993459×10¹⁰8589934592C000000??00≥1≥1C00??00???
6700000000000000000≥1≥1C00000???
68000000001.71798691×10¹¹17179869184C00000000≥1≥1C00000???
6900000000000478347264478347264C00??00≥1≥1C00??00???
70000000003.43597383×10¹¹34359738368C00000000≥1≥1C00000???
7100000000000000000≥1≥1C00000???
720256256C06553665536C01677721616777216C04.29496729×10¹⁰4294967296C6.87194767×10¹¹68719476736C1.17565350×10¹³1175653502208C1.42871383×10¹⁶1428713835603968C3.34273080×10¹⁵334273080217600C3.43764256×10¹⁹3437642565841846272C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
7300000000000000000≥1≥1C00000???
74000000001.37438953×10¹²137438953472C00000000≥1≥1C00000???
75000000000004915249152P00??00≥1≥1C00??00???
76000000002.74877906×10¹²274877906944C00000000≥1≥1C00000???
7700000000000000000≥1≥1C00000???
78000000005.49755813×10¹²549755813888C006.72314490×10¹¹67231449088C00??00≥1≥1C00??00???
7900000000000000000≥1≥1C00000???
8000000000??00000000≥1≥1C00000???
810??0??0??0??0????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
8200000000??00000000≥1≥1C00000???
8300000000000000000≥1≥1C00000???
8400000000??00??00??00≥1≥1C00??00???
8500000000000000000≥1≥1C00000???
8600000000??00000000≥1≥1C00000???
8700000000000??00??00≥1≥1C00??00???
8800000000??00000000≥1≥1C00000???
8900000000000000000≥1≥1C00000???
900??0??0??0????????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
9100000000000000000≥1≥1C00000???
9200000000??00000000≥1≥1C00000???
9300000000000??00??00≥1≥1C00??00???
9400000000??00000000≥1≥1C00000???
9500000000000000000≥1≥1C00000???
9600000000??00??00≥1≥1P00≥1≥1C00??00???
9700000000000000000≥1≥1C00000???
9800000000??00000000≥1≥1C00000???
990??0??0??0??0????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
10000000000??00000000≥1≥1C00000???
10100000000000000000≥1≥1C00000???
10200000000??00??00??00≥1≥1C00??00???
10300000000000000000≥1≥1C00000???
10400000000??00000000≥1≥1C00000???
10500000000000??00≥1≥1P00≥1≥1C00??00???
10600000000??00000000≥1≥1C00000???
10700000000000000000≥1≥1C00000???
1080??0??0??0????????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
10900000000000000000≥1≥1C00000???
11000000000??00000000≥1≥1C00000???
11100000000000??00??00≥1≥1C00??00???
11200000000??00000000≥1≥1C00000???
11300000000000000000≥1≥1C00000???
11400000000??00??00≥1≥1C00≥1≥1C00??00???
11500000000000000000≥1≥1C00000???
11600000000??00000000≥1≥1C00000???
1170??0??0??0??0????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
11800000000??00000000≥1≥1C00000???
11900000000000000000≥1≥1C00000???
12000000000??00??00≥1≥1P00≥1≥1C00??00???
12100000000000000000≥1≥1C00000???
12200000000??00000000≥1≥1C00000???
12300000000000??00≥1≥1C00≥1≥1C00??00???
12400000000??00000000≥1≥1C00000???
12500000000000000000≥1≥1C00000???
1260??0??0??0????????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
12700000000000000000≥1≥1C00000???
12800000000??00000000≥1≥1C00000???
12900000000000??00≥1≥1P00≥1≥1C00??00???
13000000000??00000000≥1≥1C00000???
13100000000000000000≥1≥1C00000???
13200000000??00??00≥1≥1C00≥1≥1C00??00???
13300000000000000000≥1≥1C00000???
13400000000??00000000≥1≥1C00000???
1350??0??0??0??0????????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C?????????
N>0x9kx9kx9kx9k2k9k9k3k9k9k3k9k9kall9k9k3k9k9k?

Smallest prime reptiles

Smallest prime reptile (9L1x8):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²
L1 9-omino≥1000000≥1P≥1P≥1P0

See Also

I 9-ominoO 9-omino