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.


Triominoes

Prime rectangles: 5.

Smallest rectangle tilings

Smallest rectangle and smallest square (3x3):

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 \ h123456789N>0
10
200
300088P
4001616P0
5005858P00
6066P156156C908908C82488248C7986679866C
700432432C00613906613906C0
80011441144C0052700885270088C00
903232P31083108C4166841668C12693951269395C≥1≥1C≥1≥1C≥1≥1C≥1≥1C
100082068206C00≥1≥1C00≥1≥1C3k
11002189621896C00≥1≥1C00≥1≥1C3k
120136136C5811058110C18944281894428C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1300154302154302C00≥1≥1C00≥1≥1C3k
1400409316409316C00≥1≥1C00≥1≥1C3k
150538538C10863781086378C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
160028814882881488C00≥1≥1C00≥1≥1C3k
1700≥1≥1C00≥1≥1C00≥1≥1C3k
18020662066C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
1900≥1≥1C00≥1≥1C00≥1≥1C3k
2000≥1≥1C00≥1≥1C00≥1≥1C3k
21078247824C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
2200≥1≥1C00≥1≥1C00≥1≥1C3k
2300≥1≥1C00≥1≥1C00≥1≥1C3k
2402942429424C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1C≥1≥1Call
N>0x3kall3k3kall3k3kall

Smallest prime reptiles

Smallest prime reptiles (3Ix2, 3Lx2):

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
I triomino06P3108P1894428C
L triomino06P2656P1665413C

Smallest common multiples

Smallest common multiple (area 6):

Common multiples' solutions count (excluding symmetric)

area36
solutions0≥2P

See Also

L1 20-ominoI triomino