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 tetromino and Z pentomino

Prime rectangles: 34.

Smallest rectangle tilings

Smallest rectangle and smallest square (6x6):

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 \ h1-456789101112N>0
1-40
5000
600022P
70000000
8022P44P88P2424P
90000088P100100P1616P
100003939P22P251251C8686P44884488P
110000000568568C800800P282282P296296P
1202626P9292C230230P13781378C84288428P3898138981C127592127592C558940558940C
1300044P236236P36783678C23862386P≥1≥1C184810184810P≥1≥1Call
14000485485C8080P90819081C82728272C≥1≥1C144760144760P≥1≥1Call
1500044P1616P2131021310C5093050930C≥1≥1C207740207740P≥1≥1Call
160224224C13451345C40644064C5031950319C463944463944C≥1≥1C≥1≥1C≥1≥1Call
170009696P45304530C??????≥1≥1C≥1≥1Call
1800054975497C22442244C??????≥1≥1C≥1≥1Call
19066P162162C10241024C??????≥1≥1C≥1≥1Call
20016601660C1642816428C6043460434C??????≥1≥1C≥1≥1Call
21000??????????????all
22000??????????????all
230120120P??????????????all
2401144411444C??????????????all
25000??????????????all
26000??????????????all
27014001400C??????????????all
2807559075590C??????????????all
29000??????????????all
3001010P??????????????all
3101281212812C??????????????all
320485300485300C??????????????all
33088P??????????????all
340286286P??????????????all
350103210103210C??????????????all
36030541343054134C??????????????all
370216216P??????????????all
38044904490C??????????????all
390772450772450C??????????????all
4001894280418942804C??????????????all
N>0xallallallallallallallall

See Also

I tetromino and Y pentominoI tetromino and A hexomino