POLYOMINO TILINGS

Polyomino Tilings

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L2 15-omino

Area: 15.

Perimeter: 20.

Size: 3x7.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 60.

Square order: 60.

Prime rectangles: ≥ 1.

Smallest rectangle tilings

Smallest rectangle and smallest square (30x30):

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
1-29
30
31-44
45
N>0
1-29
0
30
0
2
31-44
0
0
0
45
0
0
0
0
46
0
0
0
0
?
47
0
0
0
0
?
48
0
0
0
0
?
49
0
0
0
0
?
50
0
0
0
0
?
51
0
0
0
0
?
52
0
0
0
0
?
53
0
0
0
0
?
54
0
0
0
0
?
55
0
0
0
0
?
56
0
0
0
0
?
57
0
0
0
0
?
58
0
0
0
0
?
59
0
0
0
0
?
60
0
4
0
0
?
61
0
0
0
?
?
62
0
0
0
?
?
63
0
0
0
?
?
64
0
0
0
?
?
65
0
0
0
?
?
66
0
0
0
?
?
67
0
0
0
?
?
68
0
0
0
?
?
69
0
0
0
?
?
70
0
0
0
?
?
71
0
0
0
?
?
72
0
0
0
?
?
73
0
0
0
?
?
74
0
0
0
?
?
75
0
0
0
?
?
76
0
0
0
?
?
77
0
0
0
?
?
78
0
0
0
?
?
79
0
0
0
?
?
80
0
0
0
?
?
81
0
0
0
?
?
82
0
0
0
?
?
83
0
0
0
?
?
84
0
0
0
?
?
85
0
0
0
?
?
86
0
0
0
?
?
87
0
0
0
?
?
88
0
0
0
?
?
89
0
0
0
?
?
90
0
8
0
?
?
91
0
0
0
?
?
92
0
0
0
?
?
93
0
0
0
?
?
94
0
0
0
?
?
95
0
0
0
?
?
96
0
0
0
?
?
97
0
0
0
?
?
98
0
0
0
?
?
99
0
0
0
?
?
100
0
0
0
?
?
101
0
0
0
?
?
102
0
0
0
?
?
103
0
0
0
?
?
104
0
0
0
?
?
105
0
0
0
?
?
106
0
0
0
?
?
107
0
0
0
?
?
108
0
0
0
?
?
109
0
0
0
?
?
110
0
0
0
?
?
111
0
0
0
?
?
112
0
0
0
?
?
113
0
0
0
?
?
114
0
0
0
?
?
115
0
0
0
?
?
116
0
0
0
?
?
117
0
0
0
?
?
118
0
0
0
?
?
119
0
0
0
?
?
120
0
16
0
?
?
121
0
0
0
?
?
122
0
0
0
?
?
123
0
0
0
?
?
124
0
0
0
?
?
125
0
0
0
?
?
126
0
0
0
?
?
127
0
0
0
?
?
128
0
0
0
?
?
129
0
0
0
?
?
130
0
0
0
?
?
131
0
0
0
?
?
132
0
0
0
?
?
133
0
0
0
?
?
134
0
0
0
?
?
135
0
0
0
?
?
136
0
0
0
?
?
137
0
0
0
?
?
138
0
0
0
?
?
139
0
0
0
?
?
140
0
0
0
?
?
141
0
0
0
?
?
142
0
0
0
?
?
143
0
0
0
?
?
144
0
0
0
?
?
145
0
0
0
?
?
146
0
0
0
?
?
147
0
0
0
?
?
148
0
0
0
?
?
149
0
0
0
?
?
150
0
32
0
?
?
N>0
x
30k
x
?

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
1²
2²
3²
4²
5²
6²
7²
8²
9²
10²
11²
12²
13²
14²
15²
16²
L2 15-omino
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Attributions

  1. 30x30 rectangle was first found by William Rex Marshall, Packing Rectangles with Congruent Polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, pp. 181-192 (https://www.sciencedirect.com/science/article/pii/S0097316597927308).

See Also

O1 12-ominoDominoes