POLYOMINO TILINGS

Polyomino Tilings

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T 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 (5x6):

Smallest square torus (10x10):

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
0
0
0
0
6
0
0
0
0
60
0
7
0
0
0
0
0
0
0
8
0
0
0
0
80
0
0
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
40
120
0
160
0
120
11
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
300
0
0
0
0
360
13
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
700
0
0
0
0
980
15
0
0
0
0
0
240
0
320
0
40
16
0
0
0
0
720
0
0
0
0
960
17
0
0
0
0
0
0
0
0
0
0
18
0
0
0
0
1860
0
0
0
0
1920
19
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0
5080
480
0
640
0
5840
21
0
0
0
0
0
0
0
0
0
0
22
0
0
0
0
7700
0
0
0
0
9020
23
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
14300
0
0
0
0
15160
25
0
0
0
0
0
960
0
1280
0
40
26
0
0
0
0
36140
0
0
0
0
37700
27
0
0
0
0
0
0
0
0
0
0
28
0
0
0
0
67620
0
0
0
0
72380
29
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
≥100000
1920
0
2560
0
≥100000

Smallest Baiocchi figures

Smallest known Baiocchi figure (area 60):

Image Not Found

See Also

R pentominoU pentomino