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 hexomino and T1 hexomino

Prime rectangles: ≥ 24.

Smallest rectangle tilings

Smallest rectangle (3x8):

Smallest square (12x12):

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 \ h1-23456789101112131415161718N>0
1-20
300
40000
50000
6000000000
70000000
8011P0011C00
90000022P01313C0
100000033P0022P0
11000044P00000
12000000055P1010P3737C7070C109109C154154C412412C
13000066P00000841841C0
14033P001616C00387387C0039073907C00
15000002828P0184184C0102102C087308730C0≥1000≥1000C0
16011C004343C00359359C001656916569C00≥1000≥1000C0
1700006161C000002817328173C00000
1800000008282C194194P723723C16301630C28892889C45464546C5128551285C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C
190000106106C000009221492214C00000≥1000≥1000C6k
20066P00169169C0096789678C00312288312288C00≥1000≥1000C00≥1000≥1000C3k
210022P0255255C028512851C088468846C0744235744235C0≥1000≥1000C0≥1000≥1000C0≥1000≥1000C2k
22055C00392392C001657116571C00≥1≥1C00≥1000≥1000C00≥1000≥1000C3k
230000578578C00000≥1≥1C00000≥1000≥1000C6k
24011C22P33P824824C24262426C1155611556C4132041320C9279392793C194492194492C≥1≥1C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000C≥1000≥1000Call
250000??00000??00000??6k
2601010P00??00??00??00??00??3k
27001414P0??0??0??0??0??0??0??2k
2801515C00??00??00??00??00??3k
290000??00000??00000??6k
30077C1414P2121P??????????????????????????all
310000??00000??00000??6k
3201616C00??00??00??00??00??3k
33005656P0??0??0??0??0??0??0??2k
3403535C00??00??00??00??00??3k
350000??00000??00000??6k
3602828C5656P8888P??????????????????????????all
370000??00000??00000??6k
3803030C00??00??00??00??00??3k
3900168168P0??0??0??0??0??0??0??2k
4007171C00??00??00??00??00??3k
410000??00000??00000??6k
4208484C172172C312312P??????????????????????????all
430000??00000??00000??6k
4407373C00??00??00??00??00??3k
4500428428C0??0??0??0??0??0??0??2k
460137137C00??00??00??00??00??3k
470000??00000??00000??6k
480211211C476476C≥1000≥1000C??????????????????????????all
N>0x2k3k6kall6k3k2k3k6kall6k3k2k3k6kall

Smallest common multiples

Smallest known common multiple (area 24):

Common multiples' solutions count (excluding symmetric)

area6121824
solutions???≥2

See Also

Z pentomino and Y2 hexominoT1 hexomino and I heptomino