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.


W pentomino

Area: 5.

Perimeter: 12.

Size: 3x3.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Prime rectangles: ≥ 0.

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - 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 \ h
1-20
N>0
1-20
?
21
?
?
N>0
?

Smallest tori tilings

Smallest torus (2x5):

Smallest square torus (5x5):

Smallest known odd torus (5x5):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
10
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
40
0
80
20
6
0
0
0
0
280
0
7
0
0
0
0
140
0
0
8
0
0
0
0
720
0
0
0
9
0
0
0
0
720
0
0
0
0
10
0
320
0
600
2580
2720
1680
7960
10980
88560
11
0
0
0
0
3300
0
0
0
0
93060
12
0
0
0
0
9680
0
0
0
0
≥100000
13
0
0
0
0
14300
0
0
0
0
≥100000
14
0
0
0
0
36160
0
0
0
0
≥100000
15
0
2560
0
2960
60140
24520
22400
77760
≥100000
≥100000
16
0
0
0
0
≥100000
0
0
0
0
≥100000
17
0
0
0
0
≥100000
0
0
0
0
≥100000
18
0
0
0
0
≥100000
0
0
0
0
≥100000
19
0
0
0
0
≥100000
0
0
0
0
≥100000
20
0
20480
0
24480
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
21
0
0
0
0
≥100000
0
0
0
0
≥100000
22
0
0
0
0
≥100000
0
0
0
0
≥100000
23
0
0
0
0
≥100000
0
0
0
0
?
24
0
0
0
0
≥100000
0
0
0
0
?
25
0
≥100000
0
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
?
26
0
0
0
0
≥100000
0
0
0
0
?
27
0
0
0
0
≥100000
0
0
0
0
?
28
0
0
0
0
≥100000
0
0
0
0
?
29
0
0
0
0
≥100000
0
0
0
0
?
30
0
≥100000
0
≥100000
≥100000
≥100000
≥100000
≥100000
≥100000
?

Smallest Baiocchi figures

Smallest Baiocchi figure (area 20):

Image Not Found

Smallest known Baiocchi figure without holes (area 40):

Image Not Found

See Also

V pentominoX pentomino