POLYOMINO TILINGS

Polyomino Tilings

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You may also see list of all polyomino sets for which data is available here.


U pentomino

Area: 5.

Perimeter: 12.

Size: 2x3.

Is rectangular: no.

Is convex: no.

Holes: 0.

Prime rectangles: ≥ 0.

Smallest tori tilings

Smallest torus (5x10):

Smallest square torus (10x10):

Tori tilings' solutions count (including translations)

w \ h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
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
0
0
7
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
10
0
0
0
0
20
60
0
0
0
80
11
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
180
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
600
0
0
0
0
0
19
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0
20
180
0
0
0
80
0
540
0
0
20
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
22
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
2100
0
0
0
0
0
25
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
27
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
29
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
0
20
660
0
0
0
7760
0
1860
0
0
80
31
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
33
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
34
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
36
0
0
0
0
0
0
0
0
0
28440
0
0
0
0
0
37
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
40
0
0
0
0
20
2580
0
80
0
80
0
6780
0
0
20
41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
42
0
0
0
0
0
0
0
0
0
108420
0
0
0
0
0
43
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
44
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
45
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
46
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
47
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
48
0
0
0
0
0
0
0
0
0
419700
0
0
0
0
0
49
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
50
0
0
0
0
20
10260
0
0
0
80
0
25380
0
0
20
51
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
52
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
53
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
54
0
0
0
0
0
0
0
0
0
≥500000
?
?
?
?
?
55
0
0
0
0
0
0
0
0
0
20
?
?
?
?
?
56
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
57
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
58
0
0
0
0
0
0
0
0
0
0
?
?
?
?
?
59
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
60
0
0
0
0
20
40980
0
0
0
?
?
?
?
?
?
61
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
62
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
63
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
64
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
65
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
66
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
67
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
68
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
69
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
70
0
0
0
0
20
163860
0
0
0
?
?
?
?
?
?
71
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
72
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
73
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
74
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
75
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
76
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
77
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
78
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
79
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
80
0
0
0
0
20
≥500000
0
80
0
?
?
?
?
?
?
81
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
82
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
83
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
84
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
85
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
86
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
87
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
88
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
89
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
90
0
0
0
0
20
≥500000
0
0
0
?
?
?
?
?
?
91
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
92
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
93
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
94
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
95
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
96
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
97
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
98
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
99
0
0
0
0
0
0
0
0
0
?
?
?
?
?
?
100
0
0
0
0
20
≥500000
0
0
0
?
?
?
?
?
?

Smallest Baiocchi figures

Smallest Baiocchi figure (area 20):

See Also

T pentominoV pentomino