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.


P1 9-omino

Area: 9.

Size: 2x6.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: 4.

Odd order: 15.

Prime rectangles: ≥ 4.

Some facts:

Smallest rectangle tilings

Smallest rectangles (2x9, 3x6):

Smallest square (6x6):

Smallest odd rectangles (5x27, 9x15):

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 \ h123456789101112131415161718N>0
10
200
3000
40000
500000
60022P0088C
70000000
800000000
9022P044C004040C00160160C00
1000000000512512C0
11000000000000
120044C00146146C0032883288C00≥100≥100C
1300000000000000
14000000001436814368C00000
1500000624624C0015361536P00≥100≥100C00≥100≥100C
16000000005481654816C0000000
170000000061446144C00000000
18044C88C1818C7272C25862586C12561256C3855438554C296200296200C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C
19000000002035220352C00000000≥100≥100C9k
2000000000≥100≥100C00000000≥100≥100C9k
21000001060810608C00≥100≥100C00≥100≥100C00≥100≥100C00≥100≥100C3k
2200000000≥100≥100C00000000≥100≥100C9k
2300000000≥100≥100C00000000≥100≥100C9k
24001616C004403444034C00≥100≥100C00≥100≥100C00≥100≥100C00≥100≥100C3k
2500000000≥100≥100C00000000≥100≥100C9k
2600000000≥100≥100C00000000≥100≥100C9k
27088C08888C384384P182120182120C6134461344C1003610410036104C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100C≥100≥100Call
N>0x9k6k9k9k3k9k9kall9k9k3k9k9k3k9k9kall

Smallest prime reptiles

Smallest prime reptile (9P1x2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²12²
P1 9-omino≥1≥1P≥1P≥1C≥1P≥1C≥1P≥1C≥1C≥1C≥1P≥1C

See Also

O 9-ominoP2 9-omino