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.


Z tetromino and T pentomino

Prime rectangles: ≥ 0.

Smallest rectangle tilings

Smallest known 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 \ h123456789
100
20000
3000000
400000000
50000000000
6000000000022
700000000000000
80000000000440088
9000000000000000000
1000000000006666883232
1100000000002200226060
12000000000014144460602626
130000000000101012121212136136
140000000022343444294294280280
150000000000262600290290292292
16000000000074742042048908901615016150
17000000000064643232327432743480434804
180000000000168168168168434443444105241052
190000000000176176100810081963019630184164184164
2000000000883983984504502536825368406550406550
21????????00????????
22????????00????????
23????????00????????
24????????00????????
25????????00????????
26????????4848????????
27????????00????????
28????????44????????
29????????00????????
30????????00????????
31????????00????????
32????????296296????????
33????????00????????
34????????3232????????
35????????00????????
36????????00????????
37????????00????????
38????????19281928????????
39????????00????????
40????????256256????????
41????????00????????
42????????88????????
43????????00????????
44????????1284012840????????
45????????00????????
46????????19521952????????
47????????00????????
48????????9696????????
49????????00????????
50????????8650486504????????

See Also

Z tetromino and P pentominoZ tetromino and U pentomino