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.


B hexomino

Area: 6.

Size: 3x3.

Holes: 0.

Order: 18.

Square order: 96.

Odd order: ∞.

Prime rectangles: ≥ 26.

Smallest rectangle tilings

Smallest rectangle (9x12):

Smallest square (24x24):

No odd rectangles exist.

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 \ h1-8910-1112131415161718192021222324N>0
1-80
900
10-11000
12022P000
1300022P0
1400022P00
1500000000
1600000000000
1700022P00000
180001010C00022P00
1900022P0000000
20022P0000000002424C00
2100022P000000004646P0
220002020C0000000000
230001818C00000000000
24044C022P1818C66C00008080C414414C9090C252252P≥1≥1C≥1≥1C≥1≥1C≥1≥1C
2500022P00000000000≥1≥1C12k
260003636C00000000000≥1≥1C12k
270007070C0003636P000≥48≥48C000≥1≥1C4k
28022P02626C0088P00≥1≥1C00≥1≥1C00≥1≥1C3k
2900044P00000000000≥1≥1C12k
300006262C000356356P000≥1≥1C000≥1≥1C4k
31000182182C00000000000≥1≥1C12k
32088C0152152C003434P00≥1≥1C00≥1≥1C00≥1≥1C3k
330003636C000998998P000≥1≥1C000≥1≥1C4k
34000104104C00000000000≥1≥1C12k
35000412412C00000000000≥1≥1C12k
3601010C0568568C266266C150150C284284P65626562C8343683436C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
37000276276C00000000000≥1≥1C12k
38000214214C00000000000≥1≥1C12k
39000862862C0003752437524P000≥1≥1C000≥1≥1C4k
4001212C016641664C0021882188P00≥1≥1C00≥1≥1C00≥1≥1C3k
4100013561356C00000000000≥1≥1C12k
42000730730C000198484198484P000≥1≥1C000≥1≥1C4k
4300017581758C00000000000≥1≥1C12k
4402626C042784278C001473814738P00≥1≥1C00≥1≥1C00≥1≥1C3k
4500050165016C00010627521062752C000≥1≥1C000≥1≥1C4k
4600032403240C00000000000≥1≥1C12k
4700039583958C00000000000≥1≥1C12k
4803232C01015810158C67846784C1855418554C9556295562P58522525852252C103132102103132102C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
490001560215602C00000000000≥1≥1C12k
500001333813338C00000000000≥1≥1C12k
510001127211272C0003254089632540896C000≥1≥1C000≥1≥1C4k
5205050C02343423434C00626236626236P00≥1≥1C00≥1≥1C00≥1≥1C3k
530004335443354C00000000000≥1≥1C12k
540004773847738C000180078866180078866C000≥1≥1C000≥1≥1C4k
550003899838998C00000000000≥1≥1C12k
5608484C05660456604C0040528684052868C00≥1≥1C00≥1≥1C00≥1≥1C3k
57000112026112026C000996102262996102262C000≥1≥1C000≥1≥1C4k
58000151806151806C00000000000≥1≥1C12k
59000140180140180C00000000000≥1≥1C12k
600114114C0153980153980C230104230104C30243383024338C2618444226184442C5.52334895×10¹⁰5523348950C1.30027588×10¹²130027588094C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x4kxall12k12k4k3k12k4k12k3k4k12k12kall

Smallest prime reptiles

Smallest prime reptile (6Bx9):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²10²11²12²13²14²15²
B hexomino1000000036P00≥1P≥1P≥1P≥1P

Smallest tori tilings

Smallest torus (3x4):

Smallest square torus (6x6):

Smallest odd torus (3x6):

Tori tilings' solutions count (including translations)

w \ h123456789101112
100
20000
3000000
40000484800
50000000000
600002424288288120120432432
700000000000000
800002162160000≥1000≥10000000
9000000≥1000≥10000024024000≥1000≥100000
1000001201200000≥1000≥10000000≥1000≥100000
1100000000005285280000000000
120000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
130000000000≥1000≥10000000000000≥1000≥1000
1400005045040000≥1000≥10000000≥1000≥10000000≥1000≥1000
15000000≥1000≥100000≥1000≥100000≥1000≥100000≥1000≥100000≥1000≥1000
160000≥1000≥10000000≥1000≥10000000≥1000≥10000000≥1000≥1000
170000000000≥1000≥10000000000000≥1000≥1000
180000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000
190000000000≥1000≥10000000000000≥1000≥1000
200000≥1000≥10000000≥1000≥10000000≥1000≥10000000≥1000≥1000
21000000≥1000≥100000≥1000≥100000≥1000≥100000≥1000≥100000≥1000≥1000
220000≥1000≥10000000≥1000≥10000000≥1000≥10000000≥1000≥1000
230000000000≥1000≥10000000000000≥1000≥1000
240000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000≥1000

Attributions

  1. Prime rectangles taken from here http://www2.stetson.edu/~efriedma/order/index.html and here http://www.cflmath.com/~reid/Polyomino/g6_rect.html

See Also

A hexominoC hexomino