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 T1 hexomino

Prime rectangles: ≥ 84.

Smallest rectangle tilings

Smallest rectangle (6x9):

Smallest square (11x11):

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
3000
400000
50000000
6000000000
700000000000
80000000000000
9000000022P000000
1000000000000000000
1100000000000006262P003232P
12000000000000044C000000
13000000000000000000088P00
1400000002222P00000088P43384338P670670C7272P154154P
15000000000000022P2020P4040P6060P9292P≥1000≥1000P≥100≥100P
16000000000000012201220P7070P25642564P188188P562562P≥1000≥1000C≥100≥100P≥1≥1P
170000000000088P234234C120120P3232P1616P55965596P≥1000≥1000C≥100≥100P≥1≥1C≥1≥1C
18000000044C00001616C206206P51905190C954954C592592P≥1000≥1000C≥100≥100C≥1≥1C≥1≥1C≥1≥1C
190000000176176P88P0044P986986P203386203386P7285272852C2487024870C≥1000≥1000C≥100≥100C≥1≥1C≥1≥1C≥1≥1Call
20000000022P44P66P148148P22282228P1548615486C3405634056C≥1000≥1000C≥1000≥1000C≥100≥100C≥1≥1C≥1≥1C≥1≥1Call
210000000000022P1947819478C60806080P134872134872P3291832918P≥1000≥1000P≥1000≥1000C≥100≥100C≥1≥1C????all
2200000000000264264P76147614C1104411044P93689368C69626962C≥1000≥1000P≥1000≥1000C≥100≥100C≥1≥1C????all
2300000007676C0022P932932C1970819708P650146650146C≥1000≥1000C≥1000≥1000P≥1000≥1000C≥100≥100C≥1≥1C????all
24000000012641264P184184P22P212212C6275862758P83492388349238C≥1≥1C≥1≥1C≥1000≥1000C≥1≥1C≥1≥1C????all
250??????3636P8080P154154P≥1≥1C134354134354P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
260??????0000108108P≥1≥1C316846316846P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
270??????88C0052245224P≥1≥1C595090595090P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
280??????892892C009898P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
290??????85808580C26322632P162162P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
300??????384384P980980P26942694P≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????all
310??????22P0031623162P≥1≥1C≥1≥1C????????????????all
320??????216216C88P8100281002P≥1≥1C≥1≥1C????????????????all
330??????84528452C0026862686P≥1≥1C≥1≥1C????????????????all
340??????5620456204C3040030400P53685368C≥1≥1C≥1≥1C????????????????all
350??????32443244P97449744P4157841578P≥1≥1C≥1≥1C????????????????all
360??????6666C006706867068P≥1≥1C≥1≥1C????????????????all
370??????33763376C264264P10866201086620C≥1≥1C≥1≥1C????????????????all
380??????7108071080C9696C≥1≥1C≥1≥1C≥1≥1C????????????????all
390??????359336359336C310960310960C≥1≥1C≥1≥1C≥1≥1C????????????????all
400??????2424224242C8703687036C≥1≥1C≥1≥1C≥1≥1C????????????????all
410??????≥1≥1C00≥1≥1C≥1≥1C≥1≥1C????????????????all
420??????≥1≥1C50485048P≥1≥1C≥1≥1C≥1≥1C????????????????all
430??????≥1≥1C40004000C≥1≥1C≥1≥1C≥1≥1C????????????????all
440??????≥1≥1C29421202942120C≥1≥1C≥1≥1C≥1≥1C????????????????all
450??????≥1≥1C730888730888C≥1≥1C≥1≥1C≥1≥1C????????????????all
460??????≥1≥1C2424P≥1≥1C≥1≥1C≥1≥1C????????????????all
470??????≥1≥1C7377673776P≥1≥1C≥1≥1C≥1≥1C????????????????all
480??????≥1≥1C9361093610C≥1≥1C≥1≥1C≥1≥1C????????????????all
490??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
500??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
510??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
520??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
530??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
540??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
550??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
560??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
570??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
580??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
590??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
600??????≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C????????????????all
N>0x???allallallallallallallallallallallallall

Smallest common multiples

Smallest known common multiple (area 120):

Common multiples' solutions count (excluding symmetric)

area306090120
solutions???≥1

Attributions

  1. Common multiple have been found by Michael Reid

See Also

I pentomino and S hexominoI pentomino and T2 hexomino